Combine water, yeast and 1 teaspoon of sugar in a small bowl. Allow to rest for 5 minutes.
Mix 3 cups flour, remaining sugar and salt in a large mixer bowl. Add butter, 1 egg and yeast mixture. Beat 2 minutes on medium speed. Stir in 1/4 cup asiago cheese, mozzarella and 1-1/2 cups cheddar. Add enough flour to form a soft dough.
Knead on a lightly floured surface for 8 to 10 minutes, until dough is smooth and elastic. Shape dough into a ball and place in a greased bowl, turning once to cover. Cover and let rise until dough is doubled in size, about 40 minutes.
Punch dough down. Remove dough to lightly floured surface and cut in half. Roll each half into a very large circle - about 16 inches in diameter. Cut each circle of dough into 12 equal wedges. Roll each wedge into a crescent, starting at the wide end and roll to the point. Place crescents on greased baking pans. Cover and allow to rise until doubled in size, about 20 to 30 minutes.
Brush crescents with beaten egg and sprinkle with remaining 1/4 cup asiago and 1/2 cup cheddar cheese. Bake 18 to 22 minutes in a preheated 350ºF oven.
Remove from pan and cool on wire rack.