Cookies: Preheat oven to 350 degrees. Spread almonds in a single layer on a rimmed baking sheet. Bake until noticeably darkened and fragrant, 10 to 15 minutes. Transfer sheet to a wire rack; let cool completely.

Pulse almonds in a food processor until finely ground. Measure 1 1/2 cups almonds into a medium bowl; set remainder aside. Add flour and salt to bowl; whisk to combine.

In a mixer fitted with the paddle attachment, beat butter with confectioners' sugar until smooth and well combined. Beat in egg yolks and vanilla. Gradually add almond-flour mixture, beating until dough just comes together (do not overmix). Turn dough out onto a work surface and divide in half. Shape each half into a 12-inch log (about 1 3/4 inches in diameter); wrap each log in plastic. Refrigerate until firm, about 1 hour.

Measure 1/2 cup reserved almonds onto a sheet of parchment; roll each log in nuts to coat. Cut logs into 1/4-inch-thick slices, discarding ends. Transfer slices to parchment-lined baking sheets, spacing about 1 inch apart. Bake, rotating sheets halfway through, until edges are slightly browned, 18 to 20 minutes. Transfer sheets to wire racks; let cool completely.

Filling: Pulse remaining 3 cups reserved almonds and salt in a food processor on low speed, scraping down sides frequently. Mixture will look dry but continue pulsing until it reaches a smooth, spreadable consistency, 15 to 20 minutes.

In the bowl of a mixer fitted with the paddle attachment, beat together 1 cup almond butter (reserve remaining 1/2 cup for another use), confectioners' sugar, and butter until smooth, scraping down sides of bowl as needed. Transfer to a pastry bag fitted with a 1/2-inch round tip.

Pipe a small amount of filling onto bottoms of half the cookies, then sandwich with remaining cookies. Filled cookies can be stored in an airtight container at room temperature up to 1 week.