In a large bowl or the bowl of a stand mixer, combine 2 teaspoons sugar and the yeast. Add 1/2 cup of the warm water; stir to dissolve. Let stand 5 minutes until yeast is foamy, then add remaining sugar and water, oil, 3 cups of the flour and the salt. Stir to combine.
Using dough hook on medium speed, knead dough in stand mixer 5 minutes, adding enough of the remaining flour until a smooth, elastic and only slightly sticky dough forms; OR, turn dough out onto a floured surface and knead by hand 10 minutes, adding enough of the remaining flour until a smooth, elastic and only slightly sticky dough forms.
Shape dough into a ball and place in a lightly greased bowl; turn to coat. Cover with plastic wrap and let rise in a warm place 1 hour until doubled.
Punch down dough. On a lightly floured surface, divide into 8 equal pieces. Shape each piece into an elongated oval shape about 5 inches long, then transfer to lightly greased or silicone mat-lined baking sheets, leaving about 2 inches between each piece of dough.
Use a sharp serrated knife to slash tops of dough about 1/4-inch deep. Cover baking sheets with a tea towel or greased plastic wrap and let sit 30 minutes until dough is nearly doubled and puffy.
While dough is rising, heat oven to 400°F. In a medium bowl, whisk together water, melted butter, egg yolk, minced garlic, Italian seasoning, salt, garlic powder and onion powder. When dough is ready to bake, brush tops and sides with herb mixture. Sprinkle with the shredded Asiago cheese.
Bake 20 minutes, rotating pans halfway through, until rolls are baked through and cheese on top is melted and browned. Cool rolls completely on a cooling rack before slicing.