If frozen, place the raspberries in a small glass bowl and microwave on high for 30 seconds. (If using fresh berries skip this step.)
Using the tines of a fork, mash up the raspberries until they're broken apart into very small pieces and the mixture is quite liquid-y. Add the maple syrup, and chia seeds and stir well.
Put the jam in the refrigerator for at least several hours, but preferably overnight, to thicken.
Preheat the oven to 350 degrees and line two or three baking sheets with parchment paper.
Combine the gluten-free baking flour, flaxseed, baking powder, and salt in a stand mixer fitted with the paddle attachment. Add the butter, maple syrup, egg, and vanilla, and mix until a soft dough forms.
Dust a surface with some of the gluten-free baking flour and roll out half the dough to a thickness of about ⅙ inch. Using a 2½ inch round cookie cutter, stamp out cookies and place them on a baking sheet.
Repeat with the remaining dough but this time stamp out the middles of each cookie with a mini cookie cutter (about 1¼ inches in width).
Bake the cookies on the bottom rack(s) of the oven for 10-12 minutes until the cookies are light golden brown on the bottom but still pale on top. Let cool completely.
Place 1/2 teaspoon of jam on the flat side (bottom) of the cookies without the cut-out middles. Top each cookie with the remaining (cut-out middle) cookies and press them together gently.