Make a smooth paste from the garlic, lemon zest, and mustard. Transfer the mixture to a small bowl, and whisk in the egg yolks.
Gradually add the olive oil to the yolk mixture in a thin, even stream - whisking constantly. Continue to whisk until all the oil has been incorporated and the aioli is light and fluffy.
Season the aioli with the smoked paprika, salt, and pepper. Chill until ready to serve.
In a medium bowl, combine the flour, baking powder, and salt. Make a well in the center of the mixture, and add the warm butter and water. Mix to combine, the mixture will look like a shaggy mass. Knead the dough until it is smooth, 1-2 minutes.
Divide the dough into about 16 pieces (this makes for mini flatbreads to give everyone one or two...you can also make larger ones or cut them into strips, etc.), and round the dough slightly. Cover with a damp paper towel and let sit for 10 minutes. Meanwhile, heat the oil for frying.
When the dough has rested and the oil is hot, fry the breads until it is golden brown and slightly puffed up on both sides.
Drain on absorbent paper towels and garnish with coarse salt. Serve warm with the aioli.
I always have three kinds of hot sauce in my purse. I have a soft spot for making people their favorite dessert, especially if it's wrapped in a pastry crust. My newest cookbook, The Book on Pie, is out on November 10th, 2020.