In a food processor, using the S blade attachment add the dry ingredients: almond flour, coconut flour, erythritol, and salt. Blend on high speed to combine evenly - about 30 seconds. This speed will also pulse the erythritol into a thinner texture so don't skip this step.
Stop the food processor, add the soft cubes of butter, soft cream cheese, vanilla, and almond extract.
Process again on medium speed until the dough forms large crumbles of dough you can easily squeeze and bring together into a dough ball. If it's too wet add an extra tablespoon of almond flour, or if your dough is too dry add an extra teaspoon of soft cream cheese processing after any addition. The cookie dough should be soft, buttery, and easy to gather into a ball. It shouldn't be overly wet or dry.
Place the dough into a plastic bag or wrap the ball into plastic wrap. Flatten into a thick disc and refrigerate 20 minutes or overnight.
Once the dough is chilled preheat the oven to 350°F (180°C). Line one or 2 cookie sheets with parchment paper. Set aside.
Remove the dough disc from the fridge, remove plastic wrap and place the disc of dough between 2 large pieces of parchment paper. Roll with a rolling pin into a 1/4-inch thickness. The shape of the rolled dough doesn't matter as long as it is 1/4-inch thick
Peel off the top piece of parchment paper and cut-out cookies from the rolled dough using a cookie cutter.
Slide a flat tool under the cut-out cookie to transfer onto the prepared cookie sheets leaving 3 inches apart between each cookie. They won't expand in the oven.
Gather the leftover of dough to reform a ball and roll again between the same pieces of parchment paper.
Bake cookies, one sheet at a time, in the center rack of your oven for 10-12 minutes or until lightly browned around the edges but the center is yellow gold. If your oven has hot spots, the cookies may cook faster on one side so I recommend rotating the cookie sheet halfway for even baking.
The cookie will be very soft when you remove the cookie sheet from the oven and that's normal!
Cool the cookies for 5 minutes onto the cookie sheet then gently slide a spatula under each cookie to transfer on a cooling rack. They will firm up after 30 minutes on the rack and get their best texture when completely cooled down.