a.rb

# Idea taken from https://github.com/sinatra/sinatra/blob/master/lib/sinatra/base.rb#L1525-L1535
class Foo
  def run(&block)
    generate_method("something_unique", &block).call :arg
  end

  private

  def generate_method(name, &block)
    self.class.class_eval do
      define_method(name, &block)
      method = instance_method(name)
      remove_method(name)
      method
    end.bind(self)
  end

  # or

  def generate_method(name, &block)
    define_singleton_method(name, &block)
    method = method(name)
    self.singleton_class.instance_eval do
      remove_method(name)
    end
    method
  end

  def blah
    p :blah
  end
end

Foo.new.run do |arg|
  blah
  p arg
end