Warm the salted butter in a small pan over medium heat, stirring regularly, until it browns, about 2 minutes, then remove it from the heat. Look for a nutty aroma and hazelnut-brown specks at the bottom of the pan, then let the butter cool.

Heat an electric oven to 180C / 350F. Line a baking sheet with parchment paper while the oven comes to temperature.

Pulse the pecans in a food processor until they become crumbly with both fine and coarser pieces. Stop while the mixture still looks dry and pebbly rather than shiny or smooth.

Whisk the egg, allulose, and vanilla extract in a large mixing bowl until smooth. The mixture should look evenly blended with no visible streaks of egg white.

Pour in the cooled browned butter and whisk until fully incorporated. The mixture should become glossy and uniform without warm butter separating on the surface.

Stir in the pulsed pecans until a sticky dough forms. The dough should feel cohesive and tacky, similar to soft playdough rather than slick or wet.

Roll the dough into balls, arrange them on the parchment-lined baking sheet, and press each one with a fork in a crisscross pattern. Leave space between the cookies so their edges can color evenly.

Bake for 10 minutes. Remove the sheet when the cookie edges are beginning to brown and the kitchen smells richly toasted.