Index: src/wp-includes/widgets/class-wp-widget-recent-posts.php
===================================================================
--- src/wp-includes/widgets/class-wp-widget-recent-posts.php	(revision 35811)
+++ src/wp-includes/widgets/class-wp-widget-recent-posts.php	(working copy)
@@ -52,6 +52,7 @@
 		if ( ! $number )
 			$number = 5;
 		$show_date = isset( $instance['show_date'] ) ? $instance['show_date'] : false;
+		$format = ( ! empty( $instance['format'] ) ) ? $instance['format'] : null;
 
 		/**
 		 * Filter the arguments for the Recent Posts widget.
@@ -80,7 +81,7 @@
 			<li>
 				<a href="<?php the_permalink(); ?>"><?php get_the_title() ? the_title() : the_ID(); ?></a>
 			<?php if ( $show_date ) : ?>
-				<span class="post-date"><?php echo get_the_date(); ?></span>
+				<span class="post-date"><?php echo ( $format===null ? get_the_date() : get_the_date($format) ); ?></span>
 			<?php endif; ?>
 			</li>
 		<?php endwhile; ?>
@@ -109,6 +110,7 @@
 		$instance['title'] = sanitize_text_field( $new_instance['title'] );
 		$instance['number'] = (int) $new_instance['number'];
 		$instance['show_date'] = isset( $new_instance['show_date'] ) ? (bool) $new_instance['show_date'] : false;
+		$instance['format'] = sanitize_text_field( trim($new_instance['format']) );
 		return $instance;
 	}
 
@@ -124,6 +126,7 @@
 		$title     = isset( $instance['title'] ) ? esc_attr( $instance['title'] ) : '';
 		$number    = isset( $instance['number'] ) ? absint( $instance['number'] ) : 5;
 		$show_date = isset( $instance['show_date'] ) ? (bool) $instance['show_date'] : false;
+		$format    = isset( $instance['format'] ) ? esc_attr( $instance['format'] ) : '';
 ?>
 		<p><label for="<?php echo $this->get_field_id( 'title' ); ?>"><?php _e( 'Title:' ); ?></label>
 		<input class="widefat" id="<?php echo $this->get_field_id( 'title' ); ?>" name="<?php echo $this->get_field_name( 'title' ); ?>" type="text" value="<?php echo $title; ?>" /></p>
@@ -133,6 +136,9 @@
 
 		<p><input class="checkbox" type="checkbox"<?php checked( $show_date ); ?> id="<?php echo $this->get_field_id( 'show_date' ); ?>" name="<?php echo $this->get_field_name( 'show_date' ); ?>" />
 		<label for="<?php echo $this->get_field_id( 'show_date' ); ?>"><?php _e( 'Display post date?' ); ?></label></p>
+
+        <p><label for="<?php echo $this->get_field_id( 'format' ); ?>"><?php _e( 'PHP date format:' ); ?></label>
+		<input class="widefat" id="<?php echo $this->get_field_id( 'format' ); ?>" name="<?php echo $this->get_field_name( 'format' ); ?>" placeholder="<?php _e('Leave blank for default'); ?>" type="text" value="<?php echo $format; ?>" /></p>
 <?php
 	}
 }