Preheat the oven to 350 degrees F.
Bring a large pot of lightly salted water to boil. Add tortellini and cook until just tender.
Meanwhile, melt the butter in a pot over medium heat. Stir in flour until well combined. Slowly whisk in the milk. Cook, whisking constantly, until mixture comes to a simmer and lightly thickens; do not burn. Remove from heat and stir in basil or parsley and asiago and mozzarella cheese; season with salt and white pepper.
Drain the tortellini well and place in 9 by 13-inch casserole. Spoon over the sauce. Sprinkle with parmesan cheese. Bake 25-30 minutes, until golden brown and bubbling. Sprinkle with basil or parsley