Adding date shortcodes before entry content for articles in Genesis using "genesis_before_entry_content" action. http://sridharkatakam.com/how-to-add-circular-date-for-posts-in-genesis/

functions.php

add_action( 'genesis_before_entry_content','sri_add_date');
function sri_add_date () {
  if (is_home() || is_archive()) { ?>
		<div class="my-date">
			<span class="my-date-day"><?php echo do_shortcode("[post_date format='j']"); ?></span>
			<span class="my-date-month"><?php echo do_shortcode("[post_date format='M']"); ?></span>
		</div>
	<?php }
}
//* Customize the post info function
add_filter( 'genesis_post_info', 'sp_post_info_filter' );
function sp_post_info_filter($post_info) {
if (is_home() || is_archive()) {
	$post_info = 'by [post_author_posts_link] [post_comments] [post_edit]';
	return $post_info;
}}

style.css

.home .content article,
.archive .content article {
    position: relative;
}

.home .content article .my-date,
.archive .content article .my-date {
    position: absolute;
    top: -25px;
    left: -25px;
    background-color: rgba(42, 117, 213, 0.5);
    -webkit-border-radius: 28px;
    -moz-border-radius: 28px;
    border-radius: 28px;
    color: #FFFFFF;
    font-weight: bold;
    font-size: 11px;
    height: 56px;
    letter-spacing: 1px;
    line-height: 5.4;
    text-align: center;
    text-transform: uppercase;
    width: 56px;
    box-shadow: 0 1px 2px rgba(0, 0, 0, 0.1);
}

@media only screen and (max-width: 500px) {
  .home .content article,
	.archive .content article {
		padding-bottom: 6rem;
	}

	.home .content article .my-date,
	.archive .content article .my-date {
		left: 0;
		top: -60px;
	}
}

@media only screen and (max-width: 800px) {
	.home .content article .my-date,
	.archive .content article .my-date {
		right: 0;
		left: auto;
		top: 0;
	}

}