1) Position racks in the upper and lower thirds of the oven and preheat to 375˚ F. In a shallow metal pan, like a cake tin, toast the pecans, stirring once or twice, until crisp and fragrant, 8 to 10 minutes. Remove from the pan immediately, cool to room temperature, and finely chop. Measure out 2 cups chopped nuts (reserve any extra for another use).
2) In a food processor, working in batches if necessary, combine the Asiago, butter, cheddar, cornmeal, flour, black pepper, salt, and cayenne. Pulse until thoroughly blended. Turn the dough out onto a large bowl, scatter the pecans over it, and knead in the bowl until the nuts are evenly incorporated and the dough is smooth. Give the dough several whacks to knock out any air pockets.
3) Divide the dough into four equal pieces. Roll each piece out into a 12-inch cylinder about 1 inch in diameter and wrap in plastic wrap. Chill until firm, at least 2 hours. (At this point the dough can be frozen for up to 2 months. Thaw frozen dough overnight in refrigerator.)
4) To bake, preheat the oven to 400˚ F. Line several half sheet pans with parchment paper. Slice the chilled dough into ½ - inch-thick rounds, arranging the rounds as you go on the prepared pans, taking a moment to shape each cookie more perfectly round with your fingers, and spacing them about 1 ½ inches apart. Bake, exchanging the positions of the pans on the racks from top to bottom and from front to back, halfway through baking, until the cookies are lightly browned, about 10 minutes. Transfer to racks and cool to room temperature.
5) Store the cookies airtight at room temperature; the cookies will keep for at least a week and actually develop more flavor after sitting for a day or two. Or the cookies may be frozen in an airtight container for up to one month.