Preheat the oven to 350F (180 C / gas mark 4) with a rack in the middle position. Line 2 baking sheets with parchment and set aside.

Sift together the flour, baking powder, salt, and soda. Set aside.

Use a stand mixer with the paddle attachment to make the dough. Cut the almond paste into thick slices or big chunks. Put them in the mixer with the sugar. On low speed, mix the ingredients together until the almond paste has broken up into big pea-like pieces.

Pause to add the butter. On medium-low speed, beat the ingredients until fluffy, about 2 minutes.

Add the sifted dry ingredients. Mix on low speed until just combined (you no longer see flour bits). Add the almonds and use the lowest speed (“Stir” on a Kitchen Aide) to mix into the dough.

Put 2 to 3 tablespoons of powdered sugar in a small bowl or on your work surface. For slightly gnarly/textured cookies, pinch off balls of dough – each the size of a big cherry tomato (1.5 inch / 3.75 cm wide). Roll in powdered sugar, then place on the prepared sheet pan, spaced 2 inches (5 cm) apart. Flatten each ball slightly as you work. (If you want neater cookies, squeeze and roll the dough into a fat log and cut crosswise into pieces. Roll them into balls, coat in the sugar, etc. See the photo above.)

Bake for 12 to 15 minutes until golden brown at the edges. Cool completely on a wire rack. Store in an airtight container for several days.