Frangipane: Preheat oven to 350 degrees. Lightly toast pecans on a rimmed baking sheet, tossing halfway through, until slightly darkened in color and fragrant, 6–8 minutes. Let cool; set 1-1/4 cups pecans aside for making dough.

Pulse granulated sugar and remaining ¾ cup pecans in a food processor until nuts are very finely ground (be careful to stop before they become a paste), 30-60 seconds. Add egg white and pulse just to blend, then add butter, espresso powder, salt, and almond extract. Pulse just until mixture is smooth and combined. Scrape frangipane into a small bowl and chill at least 30 minutes before using.

Do Ahead: Frangipane can be made 3 days ahead. Cover and keep chilled. You will have more than you need. You can spread it on toasted bread, brioche or croissants, then bake until lightly browned. Or you just eat it with a spoon like I did.

Dough and Assembly: Pulse flour, salt, baking powder, and 1 cup reserved pecans in a clean food processor until nuts are very finely ground, about 1 minute.

Beat butter, granulated sugar, and ¼ cup powdered sugar in the bowl of a stand mixer fitted with paddle attachment (or use an electric hand mixer with regular beaters) on medium-high speed until light and fluffy, about 4 minutes. Add egg yolk and vanilla and beat until combined and no streaks remain.

Reduce speed to low and add dry ingredients. Beat just until incorporated, about 1 minute. Cover bowl with plastic wrap or wax paper and chill dough until it’s firm enough that you can scoop it and it will hold its shape, 30-45 minutes.

Place racks in upper and lower thirds of oven; preheat to 350 degrees. Place ½ cup powdered sugar in a shallow bowl. Working in batches, scoop out tablespoonfuls of dough and roll into balls between your hands, then roll in powdered sugar, knocking off any excess. Transfer to 2 parchment-lined baking sheets as you work, spacing 2” apart.

Bake cookies until puffed but edges are still soft, 6-8 minutes. Carefully remove from oven and make an indent in the center of each cookie with the handle end of a wooden spoon or a similar heatproof object. Spoon a heaping ½ teaspoonful of frangipane into each and top with a pecan half from reserved ¼ cup. Return cookies to oven and continue to bake until edges are sent and very lightly browned 6–8 minutes longer. Let cool on baking sheets.

Just before serving, dust cookies with more powdered sugar if desired.

Do Ahead: Cookies can be baked 5 days ahead. Store airtight at room temperature.