My baked beignets tasted like leavened bread squares, lacking in any richness and which powdered sugar could not save. I think that baked beignets are still possible, but only if we reverse engineer them to make up for the fat that goes into deep frying. I'll be frank here -- I like deep fried foods, but I don't have a kitchen that would fare well with deep frying. Too much wood flooring and 100-year-old plaster than I care to wipe down. This would be seriously beyond the capacity of any spatter-proof lid to hold back as well. So a reverse engineered baked beignet would require a few modifications. Heavy cream and evaporated milk instead of just 'milk'. Lots of butter. Eggs. Enough eggs to make challah. Really, I imagine the ideal baked beignet to be closer to mini-brioches with sugar on top. Like so.
The recipe I linked to, above, calls for shortening. I can't abide Crisco -- it just smells and taste weird. So we're looking at either beef tallow (time to collect broth fats...) or butter. Given how I felt the beignets didn't rise enough both times I baked, we're looking at tallow. Or combination tallow and schmaltz? Oooooh.