Mix together yeast, sugar, and warm water and stir together. Let sit 5 minutes until it smells yeasty and bubbles. Meanwhile, in a small saucepan over low heat, or in a bowl in the microwave, melt butter and heat milk together until warm (like lukewarm bathwater, about 100-115° F). Let cool slightly.
In a large bowl, stir together yeast and milk mixture, plus eggs, garlic powder, and 1 cup semolina pasta flour. Stir until smooth, and then stir in 1 cup shredded asiago cheese until incorporated. Then add rest of flour and stir until it forms a stiff dough and you can’t stir it any more with a spoon. Knead ten minutes on countertop, letting dough rest 5 minutes if it gets tough, and then knead 2-3 more minutes. Put in oiled bowl to rise, turning to coat the dough with oil. Cover with plastic wrap and put in warm, draft-free place to rise until doubled, about 1-1 ½ hours.
Preheat oven to 375°F. Punch down risen dough, and knead 1 minute. Divide dough into three pieces, and roll each piece into a long snake, about 16 inches long and 2 inches wide. If dough resists rolling or stretching, let it rest a few minutes and try again. Pinch together the three ends of the pieces, and gently braid them. When you reach the end, pinch the ends together and turn under. Cover loaf with lightly oiled plastic wrap and let rise 30 minutes in a warm, draft-free place.
Before baking, brush with milk and sprinkle with ¼ cup asiago cheese and finely chopped prosciutto. Bake 35-45 minutes, checking after 35 minutes and covering loosely with aluminum foil if browning too quickly. The top will get dark brown and the prosciutto will get very dark and crispy. When finished, the loaf will sound hollow when tapped (even where the braided pieces meet). Let cool, and serve slightly warm or at room temperature, or toasted.
Keep covered in a cool place up to 2 days or in refrigerator for 4-5 days. You can also substitute other sharp cheeses such as parmesan, pecorino, or Romano.
Makes one large braided loaf.
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