Preheat the oven to 375 degrees F (190 degrees C). Grease a 13x18-inch baking sheet.
Beat white sugar and 1 cup butter together in a bowl until fluffy. Add eggs 1 at a time, mixing after each addition. Add 2 teaspoons almond extract and vanilla extract; mix well.
Whisk flour, 3/4 teaspoon salt, and baking soda together in a bowl. Add to egg mixture and stir until just combined. Spread onto the prepared baking sheet.
Bake in the preheated oven until a toothpick inserted into the cookie comes out clean, 10 to 15 minutes; they won't look done. Cool completely, about 30 minutes.
Beat 1/2 cup butter in a bowl using an electric mixer until smooth and creamy. Add 1 teaspoon almond extract and 1/4 teaspoon salt. Add confectioners' sugar, 1 cup at a time, mixing until combined. Add heavy cream, 1 tablespoon at a time, until frosting reaches a smooth, spreadable consistency. Spread frosting over cooled cookie bars.