Whisk together the hazelnut flour, all-purpose flour, baking powder, and salt in a medium bowl.
Combine butter and sugars in a large bowl and beat vigorously until light and fluffy, about 2 to 3 minutes. Add the egg and chopped rosemary, then beat again until well-blended, another 30 seconds. Finally, fold in the flour mixture until just incorporated. Divide dough into two or three balls, pat them into discs, and wrap each in plastic wrap. Chill the dough in the fridge for at least 1 hour and up to 2 days.
Heat oven to 350°F. Line two baking sheets with parchment paper or silicone baking mats. Roll out a disc of dough to about 1/8- or 1/4-inch thick, depending on your preference. Unlike pie crusts, which I generally roll out between sheets of parchment, I found this to be easiest on a well-floured surface, sprinkling flour over the top and lifting the bottom to re-flour as needed. (The latter makes cutting and removing the cookie rounds much easier.) Cut out cookie rounds using a 2-inch cookie cutter of your choice. For half the rounds, use a smaller cookie cutter (around 3/4 inch) to cut patterned holes — these are the windows for the cookie “lids.” Save the minis to make miniature cookie sandwiches (or just to nosh!) If the dough becomes too soft as you’re using it, just pop it into the freezer for a few minutes to firm it up again.
Place the “lids” and cookie holes on one baking sheet and the whole cookies on another, since the whole cookies may take a little longer to bake. Bake both sheets of cookies until golden at the edges, about 10 minutes for the bottoms and 8-9 for the lids. Cool on baking sheets for a few minutes, then transfer to a wire rack to finish cooling. Repeat with remaining dough; you can re-chill and re-roll cookie scraps as many times as needed.
If powdering the lids, arrange the lids (or all the cookies, if you prefer) on a baking rack with a tray or paper underneath to catch the excess sugar. Sift powdered sugar over top as desired.
While the cookies are cooling, make the caramel. Prepare a bowl of ice water and set it aside within easy reach. Combine sugar and water in a heavy-bottomed saucepan over medium heat. Stir just until sugar dissolves, then let simmer, without stirring, until the mixture just turns golden. Remove immediately from heat and add butter (be careful, as it may sputter). Swirl until the butter is dissolved, then add the creme fraiche or heavy cream, vanilla extract, and salt. Return to heat, reduce heat to low and stir until the heavy cream is fully dissolved. Drop a small spoonful of the caramel into the ice water and touch it — if you can form it into a pliable ball, it’s done. (See Izy’s tutorial for step-by-step GIFs.)
Working quickly, while the caramel is still soft, drop about a teaspoon of caramel onto each of the bottoms of the cookies, then place a lid on top and press gently to seal. Sprinkle a bit of flaky salt over top if you like. Enjoy once the caramel is cool. Cookies will keep for a week in an airtight container and freeze for up to 3 months.