Preheat the oven to 350°F (175°C). Line one or two baking sheets with parchment paper and set aside.
In a medium bowl, whisk together the all-purpose flour, baking powder, and kosher salt until evenly combined.
In a large bowl or the bowl of a stand mixer, beat the room-temperature unsalted butter and granulated sugar on medium-high speed until light and fluffy, about 2–3 minutes.
Add the egg and beat until incorporated. Add the vanilla and pistachio extracts and mix to combine.
Add a few drops of green food coloring and mix until the color is evenly distributed. Add more drops as needed — the dough will lighten when the flour is added.
Add the finely chopped raw shelled pistachios and the dry flour mixture. Mix on low speed just until the dough comes together into a crumbly mass.
Turn the dough out onto a lightly floured surface and knead gently until it forms a smooth ball. If the dough feels too soft to roll, cover and refrigerate for up to 30 minutes.
On a lightly floured surface, roll the dough to 1/4-inch thickness.
Cut the dough into shapes with cookie cutters and arrange the cut cookies on the prepared baking sheets, leaving about 1 inch between cookies.
Bake 7–9 minutes, or until the bottoms just begin to brown. Check after about 6 minutes if using lightweight pans. (If you prefer crunchier cookies, bake 1–2 minutes longer. For less browning, you can double up lighter-weight baking sheets.)
Transfer the cookies to a wire rack and let cool completely before decorating.
To make the coating, place the green candy melts or white chocolate and the 2 teaspoons unflavored vegetable shortening in a microwave-safe bowl or use a double boiler. Melt at 50% power in 30-second bursts, stirring between each burst, until smooth and fluid; or melt and stir until smooth in the double boiler. Keep the melted coating warm and fluid while you work.
Use a fork to drizzle the melted coating over the cooled cookies. Immediately sprinkle with your chosen sprinkles so they adhere before the coating sets.
Let the coating set completely. Store cookies at room temperature in an airtight container for up to 5 days.