1. In a medium saucepan, melt the butter over medium heat. Keep cooking it after it has melted, stirring frequently, until it begins to smell nutty and pale brown flecks appear at the edge of the pan, which takes a few minutes. Once these reach a dark beige/medium brown color, remove from heat. Pour 1/4 cup of this browned butter mixture into a large bowl for the cookie dough. Place the rest (4 to 5 tablespoons) in a small-medium dish and freeze it until needed for the filling.

2. Let the browned butter cool slightly in the large bowl, then whisk in sugar, vanilla extract, and scraped vanilla bean seeds (if using). Whisk in eggs, one at a time, followed by salt and baking powder. Switch to a spoon and add first cup flour, stirring to combine. Repeat with second cup of flour, then 1/4 cup. Knead the dough in with your hands if it becomes too stiff to stir. Divide dough into two parts and wrap each in plastic. Refrigerate for 2 hours or up to a few days, or freeze for 20 to 30 minutes until firm but not frozen.

3. In a food processor, place nuts, flour, salt, and sugar and run the machine until the nuts are finely ground but not yet forming a paste. Scrape the frozen browned butter into the machine and run until combined. Add egg and any flavorings and run until a smooth paste forms. Scrape hazelnut paste into the dish and place in the fridge until needed.

4. Heat oven to 350°F and line two baking sheets with parchment paper or a nonstick baking mat. Roll chilled dough out on a floured counter until 1/8-inch thick. Cut into 3-inch circles. In the center of each circle, dollop a scant teaspoon of hazelnut paste and a 1/2 teaspoon dab of apricot jam. Fold sides up, forming a triangular shape and pinching the corners closed well. Arrange on baking sheet with an inch apart between cookies.

5. Bake cookies for 11 minutes, check the color, and return to the oven, a minute at a time, until golden at the edges. Let cool on racks. Cookies keep in an airtight container at room temperature for up to a week, longer in the freezer.