Step 1

Place racks in upper and lower thirds of oven; preheat to 350°. Toast nuts and ¼ cup sesame seeds on a rimmed baking sheet on upper rack, tossing halfway through, until golden brown, 8–10 minutes. Let cool.

Step 2

Stir together ancho powder and agave syrup in a small bowl. Whisk flour, baking powder, and cinnamon in a medium bowl to combine. Using an electric mixer on medium-high speed, beat butter, sugar, and salt in a large bowl, scraping down sides and bottom of bowl as needed, until light and creamy, about 3 minutes. Add egg yolks and vanilla and beat until incorporated, about 1 minute. Scrape in ancho mixture and beat until smooth and creamy, about 1 minute. Reduce speed to low, add dry ingredients, and beat to combine. Add dried fruit, chocolate, and toasted nuts and sesame seeds; mix with a wooden spoon until evenly distributed.

Step 3

Divide dough in half. Working one at a time, roll each piece into a 10"-long log. Wrap each log tightly in plastic and roll across work surface to make as smooth and cylindrical as possible. Place on a rimmed baking sheet and freeze until surface is firm, about 20 minutes.

Step 4

Slap a log down onto counter to create a flat side; roll over and slap again to flatten another side (you’re aiming for a triangular shape). Repeat to create third side of the triangle. Tap against counter to smooth if needed, then tap ends to flatten. Repeat with second log. Return logs to baking sheet; freeze until firm, about 15 minutes.

Step 5

Working one at a time, unwrap logs and brush sides with egg white. Working on baking sheet, sprinkle sides with remaining 1 cup sesame seeds and gently press to coat. Surface should be covered; use more sesame if needed. Freeze logs on baking sheet, uncovered, until surface is very firm but not frozen solid, about 1 hour.

Step 6

Preheat oven to 350°. Slice a log crosswise into ¼"-thick triangles and divide cookies between 2 parchment-lined baking sheets, spacing 1" apart. (If dough is soft or starts to lose its shape, freeze 10 minutes before continuing.) Bake cookies, rotating baking sheets top to bottom and back to front halfway through, until edges are just set, about 10 minutes. Let cool on baking sheets. Transfer cookies to a platter or airtight container and line baking sheets with fresh sheets of parchment paper. Repeat process with remaining dough.

Step 7

Do Ahead: Dough can be rolled into logs 3 days ahead; refrigerate. Transfer to freezer 30 minutes before slicing. Cookies can be baked 1 day ahead; store airtight at room temperature.