Preheat your oven to 350°F (175°C) and line two large baking sheets with parchment paper.
In the bowl of a stand mixer, cream the softened butter and granulated sugar on medium-high speed until light and fluffy (about 3 minutes).
Beat in the eggs one at a time, ensuring each is fully incorporated before adding the next.
Add the ricotta cheese, 1 teaspoon of vanilla extract, and 1/2 teaspoon of almond extract. Mix on medium speed until the batter is smooth and well combined.
Turn the mixer to low speed and gradually add the self-rising flour. Mix just until the dry streaks of flour disappear. The dough will be very sticky.
Using a cookie scoop, drop tablespoon-sized mounds of dough onto the prepared baking sheets, leaving 2 inches of space between each cookie.
Bake for 12-15 minutes. The bottoms should be lightly golden, but the tops will remain pale and cake-like. Do not overbake.
Let the cookies rest on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.
To make the glaze, whisk the powdered sugar, milk, and 1/4 teaspoon of almond extract in a small bowl until smooth and thick.
Dip the tops of the completely cooled cookies into the glaze. Place them back on the wire rack and immediately top with holiday sprinkles. Let sit until the glaze hardens.