Preheat the oven to 350°F and line a baking sheet with parchment paper.
Simmer blueberries, allulose, and lemon juice in a small saucepan over medium heat for 4 to 5 minutes, mashing until jammy. Stir in xanthan gum and cool for 10 minutes.
Stir almond flour, coconut flour, powdered allulose, baking powder, and salt in a bowl.
Add softened butter, egg, vanilla extract, lemon zest, and chopped basil. Mix until the dough is soft and fragrant.
Scoop 12 cookies onto the baking sheet and press a small well into each one.
Spoon the blueberry swirl into the wells and lightly drag a little into the cookie tops.
Bake for 11 to 13 minutes, until the edges are lightly golden. Cool completely for the best soft-chewy texture.