Heat the Milk: In a small saucepan over medium-low heat, warm the milk until bubbles form around the edge. Remove from heat.
Add Butter and Almond Extract: Stir in the butter and almond extract until the butter melts completely. Let it cool while you prepare the dry ingredients.
Mix Dry Ingredients: In a stand mixer with a dough hook, combine 2 1/2 cups flour, yeast, sugar, and salt.
Combine Wet and Dry Ingredients: Add the egg and the milk mixture to the dry ingredients. Mix well, scraping down the bowl as needed.
Add Remaining Flour: Gradually add the remaining 1 cup of flour, 1/2 cup at a time, mixing well after each addition. Beat for 5 minutes on medium speed.
Knead and Rise: Place the dough on a floured surface, knead it into a ball, and then transfer it to a large bowl. Cover with plastic wrap or a damp cloth and let it rise in a warm place for 40 minutes.