1 cup (2 sticks) unsalted butter, at room temperature
1 cup sugar
2 large eggs
1 teaspoon pure vanilla extract
3 cups all-purpose flour, plus more for dusting (see Cook's Note)
1/4 cup assorted brightly colored hard candies (about 8 pieces)
Cream the butter and sugar in a stand mixer fitted with the paddle attachment on medium-high speed until smooth, about 2 minutes. Reduce the speed to low and add the eggs 1 at a time, mixing after each addition until fully incorporated. Add the vanilla and then slowly mix in the flour until well combined, scraping down the sides of the bowl as needed. Remove the dough, press into a flat rectangle, wrap in plastic wrap and refrigerate for at least 1 hour and up to overnight.
Position oven racks in the top and bottom thirds of the oven and preheat to 350 degrees F. Line 2 baking sheets with parchment.
Cut the dough into thirds, wrap 1 piece back in the plastic wrap and return it to the refrigerator. Dust your work surface and the remaining 2 pieces of dough well with flour and roll out each to 3/16 inch with a rolling pin, moving the dough and dusting the top and bottom with additional flour if it becomes sticky. Cut out as many large stars as possible with a 4-inch star cookie cutter and place on the prepared baking sheets. Gather the scraps and reroll once to cut out more cookies. You should have a total of 12 stars. Cut a small star out of the middle of each large star with a 2-inch star cookie cutter and reserve for another use. (You can chill and bake the small stars separately or freeze for later.) Refrigerate the baking sheets until the dough is firm, 15 to 20 minutes.
Meanwhile, separate the candy by color and place each color in a separate resealable plastic bag. Place a kitchen towel over the bags and crush the candy into small pieces using a rolling pin or meat mallet; do not pulverize. Fill the cut-out areas of the cookies two-thirds full with the crushed candy.
Bake the cookies, rotating the baking sheets from top to bottom and front to back halfway through, until light golden brown and the candy has melted, 12 to 15 minutes. Cool on the baking sheets for 5 minutes before transferring to wire racks to cool completely. Repeat the rolling, cutting, filling and baking process with the remaining piece of dough.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)