In a bowl, combine the flour, powdered sugar, baking soda, and salt.
Add in shortening and butter. Mash with a fork until no dry ingredients remain. Add extracts and combine thoroughly.
The dough shouldn't be too soft. The consistency should be like a thick cookie dough. If you find it is very soft, add equal parts flour and powdered sugar, 1 Tablespoon at a time until it gets thicker and less sticky. It should be tacky but not sticky, and slightly firm.
Refrigerate the topping for 20 minutes to stiffen up a bit. This will make it easier to work with when it comes time to pressing it out.
After the dough is doubled, punch down and cut into 8 equal pieces. Shape into tight balls. Cover with lightly oiled plastic wrap, a damp cloth, or an upside-down pan or bowl so they don't dry out while pressing out the topping.
Divide the refrigerated topping into 8 equal round pieces. Make sure they're slightly cold or you may have problems with sticking. Press with a tortilla press or roll out to about 1/8" thick. Place topping disk over each ball and press down lightly to adhere and flatten dough ball just a bit. (Not too hard) Stamp each top with a concha stamp, or use a round cutter or knife to lightly cut your design.
Proof the dough balls until visibly bigger and puffy. Heat oven to 350. Bake conchas for 18-20 minutes, Keep an eye on the topping and try to catch it before it browns. Buns should register 190ºF with a probe thermometer when poked in the center.
Cool on a wire rack. Keep covered on the counter for up to 4 days. The topping will soften as it sits.