In a medium saucepan, melt the butter over medium heat. Add the flour and stir just until mixed.
Add the evaporated milk, regular milk and chicken broth and cook, stirring often, until the sauce thickens and begins to simmer.
Remove from heat and add the Asiago cheese, stirring just until the cheese melts smoothly into the sauce. Set aside.
Heat the olive oil in a large, preferably non-stick, skillet. Add the cubed chicken, parsley and garlic, and continue to cook, stirring frequently, until the chicken is opaque and cooked through — 8 to 10 minutes. Add the Asiago sauce and season with salt and pepper. Stir to combine.
Meanwhile, cook the bow tie pasta in a large pot of boiling salted water until tender but not mushy.
Drain well in a colander, then return pasta to the pot and add the chicken and Asiago sauce. Toss to combine and serve immediately, with additional grated Asiago cheese sprinkled on top, if desired.
If making ahead, transfer the sauce to a covered container and refrigerate. When you are ready to serve dinner, place sauce in a large saucepan and heat very gently over low heat, stirring often. Don’t let it boil.