Preheat your oven to 350°F (175°C). This ensures that your cookies bake evenly.
In a large mixing bowl, combine the softened unsalted butter and brown sugar. Use an electric mixer to beat them together until the mixture is light and fluffy, about 2-3 minutes.
Add in the room temperature egg and 1/2 teaspoon of vanilla extract. Mix until well combined.
In another bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Gradually add the dry mixture to the wet mixture, mixing until just combined.
Gently fold in the sour cream and chopped cashews. Be careful not to overmix; you want to keep the dough light and airy.
Using a cookie scoop, drop rounded tablespoons of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden. The centers may seem slightly underbaked, but they will firm up as they cool.
Remove the cookies from the oven and allow them to cool on the baking sheets for 5 minutes before transferring them to a cooling rack.
In a small bowl, whisk together the half and half cream, 1/4 teaspoon vanilla extract, and confectioner’s sugar until smooth. Adjust the consistency by adding more cream or sugar as needed.
Once the cookies are cool, drizzle or spread the icing on top and garnish with cashew halves for an extra touch.