In a stand mixer fitted with the paddle attachment (or using a hand mixer), beat the butter, granulated sugar, and powdered sugar for 2–3 minutes, until pale, creamy, and fluffy.
Beat in the egg, vanilla bean paste, and almond extract until fully combined.
Mix flour, baking powder, and salt together. Add to the mixer on low until a soft dough forms. It should look smooth and play-dough like, not sticky.
Divide the dough in half. Roll each half between two sheets of parchment paper to ¼ inch thick (6 mm) for soft centers or ⅛ inch (3 mm) for crispier cookies. Rolling between parchment prevents sticking and eliminates the need for extra flour.
Cut cookies in desired shape and place on a parchment lined baking sheet.
Chill the cut out sugar cookies for 1–2 hours (or freeze 20–30 minutes). This helps the cookies keep their shape.
Preheat oven to 350°F (175°C).
Bake 8–11 minutes, depending on size and thickness. Edges should be just barley turning golden brown. The centers should look set but pale.
Let cool on the baking sheet for 5 minutes, then move to a cooling rack to finish cooling.
Whisk powdered sugar, heavy cream, melted butter, corn syrup, vanilla, and salt until smooth and glossy.
Add more cream (½ tsp at a time) for thinner flood icing.
Add more powdered sugar for a thicker outline icing.
Divide and color with gel food coloring if desired.
Ice cooled cookies and let set 6–8 hours (or overnight for fully firm icing).
