A method for dynamically generating Settings Fields in WordPress through the use of an anonymous function assigned to a variable variable. This could be expanded to generate different input types (hidden, text, textarea, and maybe a select), and to dynamically generate Setting Sections and Section Callbacks.

dynamically-generated-settings.php

<?php

/*
 * Dynamically Generated Checkboxes in a WordPress Settings Page
 *
 * This file is fully functional and ready to be used in a plugin or theme to generate this Settings Page
 *
 */

Class Pizza_Shop {

	//Set up Toppings Array to be used to generate checkboxes
	static $toppings = array(
		"crust" => array(
			"thick", "thin",
		),
		"meat" => array(
			"beef", "pepperoni", "sausage", "canadian bacon",
		),
		"veggies" => array(
			"mushrooms", "onions", "olives", "tomatoes",
		),
		"other" => array(
			"extra cheese", "extra sauce", "anchovies",
		),
	);

	//This method takes two parts of the settings field name and assembles them. (e.g., "meat_beef")
	public static function input_setup( $choice_title ){
		$options = get_option('pizza_shop_settings');
		$value = (isset( $options[$choice_title] ) ? $options[$choice_title] : '');
		return $value;
	}

}

//Add Menu Page
add_action( 'admin_menu', 'pizza_shop_add_toppings_menu' );

function pizza_shop_add_toppings_menu() {
	add_menu_page( __( 'Pizza Shop Settings' ), __( 'Pizza Shop' ), 'administrator', basename(__FILE__), 'pizza_shop_general_settings' );
}

//Register Setting and add Sections
function pizza_shop_render_fields() {
	register_setting( 'pizza_shop_settings', 'pizza_shop_settings', 'validate_pizza_shop_settings' );
	add_settings_section('meat_section', __( 'Meat Toppings', 'pizza_shop' ), 'meat_section_cb', __FILE__ );
	add_settings_section('veggies_section', __( 'Veggie Toppings', 'pizza_shop' ), 'veggies_section_cb', __FILE__ );
	add_settings_section('other_section', __( 'Other Toppings', 'pizza_shop' ), 'other_section_cb', __FILE__ );
}

add_action( 'admin_init', 'pizza_shop_render_fields' );

//The basic markup for the Settings Page.
function pizza_shop_general_settings() {
	?>
	<div id="pizza_shop-settings-wrap" class="wrap">
		<div class="icon32" id="icon-options-general">
			<br />
		</div>
		<?php _e( '<h2>Pizza Shop Toppings</h2>', 'pizza_shop'); ?>
		<form method="post" action="options.php" enctype="multipart/form-data">
			<?php settings_fields( 'pizza_shop_settings' ); ?>
			<?php do_settings_sections( __FILE__ ); ?>
			<p class="submit">
				<input name="Submit" type="submit" class="button-primary" value="<?php esc_attr_e( 'Send Me A Pizza!' ); ?>" />
			</p>
		</form>
	</div>
	<?php
}

//Here's where all the action happens
function generate_toppings_checkboxes() {
	
	//Fetch Toppings Array
	$toppings_array = Pizza_Shop::$toppings;
	
	//Now we're going to extract each combination of type and choice (e.g., "meat" and "Beef")
	foreach ( $toppings_array as $type => $choices ) {
		$toppings_type = $type;
		
		//foreach choice, we will generate a checkbox and an add_settings_field function
		foreach ( $choices as $choice ) {

			//start the string that we'll be using for ids and names.  (e.g., meat_beef)
			$choice_title = strtolower( $type . '_' . $choice );
			
			/* Here is where the action happens.  
			 * I'm using (unneeded) brackets here to help visualize what's happening.
			 * This variable variable basically generates "$meat_beef"
			 *
			 * Then, we're using this variable to hold an anonymous function.
			 * "use" is basically how we pass variables to an anonymous function.
			 */
			${$choice_title} = function() use ( $type, $choice, $choice_title ) {
				$options_value = Pizza_Shop::input_setup( $choice_title );
				echo "<input type='checkbox' id='pizza_shop_settings[". esc_attr( $choice_title ) . "]' name='pizza_shop_settings[" . esc_attr( $choice_title ) . "]' value='1' " . checked( 1, isset( $options_value ) ? $options_value : 0, false ) ." />";
			};
			
			/*Capitalize the choice ("beef") so we can present it as the field title 
			 *(the second parameter in add_settings_field)
			 */
			$cap_choice_title = ucwords( $choice );
			
			/* The third parameter of add_settings_field takes a function name, 
			 * we're using the dynamically generated variable to reference the anonymous function above.
			 */
			add_settings_field( $choice_title, esc_html__( $cap_choice_title, 'pizza_shop' ), ${$choice_title}, __FILE__, $type . '_section' );
		}
	}
}

add_action( 'admin_init', 'generate_toppings_checkboxes' );

//Functions required by the add_settings_section()s above
function meat_section_cb() {}
function veggies_section_cb() {}
function other_section_cb() {}

//Chincy validation function
function validate_pizza_shop_settings( $input ) {
	return $input;
}