1. Make the dough: In the bowl of a standing mixer fitted with the paddle attachment, beat the butter, sugar and salt at medium-high speed until light and fluffy, about 2 minutes. Add the eggs and vanilla and beat until combined, scraping the side of the bowl with a rubber spatula as needed.
2. In a small bowl, whisk the flour with the baking powder. Add the flour mixture to the butter mixture in 3 stages, beating at low speed until each addition is just combined. Divide the dough in half and flatten each portion into a disc. Wrap the discs in plastic wrap and refrigerate for 1 hour.
3. Make the rolling mix: In a spice mill, grind the peppercorns with the sea salt until fine. In a small bowl, whisk the pepper mixture with the sugar and flour.
4. Preheat the oven to 375˚ and line 2 baking sheets with parchment paper. Remove the dough from the refrigerator. Sprinkle a few tablespoons of the rolling mix onto a clean work surface. Dust the rolling pin and the top of 1 disc of the dough with additional rolling mix. Roll the dough out until it is ⅓-inch thick. Using a 2-inch cookie cutter, punch out the cookies. Reroll the scraps and punch out the remaining cookies. Repeat with the other disc of dough.
5. Arrange the cookies one-quarter-inch apart on the prepared baking sheets. Bake the cookies until the edges are golden brown, about 8 minutes, rotating the baking sheets after 4 minutes. Transfer the baking sheets to a cooling rack and let cool completely. Serve the cookies immediately or store in a resealable container for up to 1 week.