Combine 1 tbs Italian seasoning, salt and pepper then rub on all sides of the chicken.
Melt the butter in a large, deep skillet or saute pan over medium-high heat. Brown the chicken very well on both sides; about 8-10 minutes. Remove to a plate. Pour off all but 1 tbs of fat from the pan.
Add the garlic and the remaining 1 tbs of Italian seasoning to the pan and cook until fragrant, about 1 minute.
Deglaze the pan with the wine, scraping up the browned bits at the bottom of the pan. Cook until reduced by half; about 3-5 minutes. Stir in the stock and half-and-half and heat to a simmer.
Add 1 cup of the Asiago and the cream cheese, whisking until the cheeses melt and sauce is slightly thickened.
Return chicken to the pan, bring to a simmer, then cover, reduce heat to low and cook for 30-35 minutes. Top chicken with remaining 1/4 cup of Asiago.
For slow cooker: after browning, place chicken in a 4-6 quart slow cooker. Continue making sauce as in main recipe. Pour the sauce over the chicken, cover and cook on low for 3 1/2-4 hours.
I always use low-sodium stocks. I find Better Than Bouillon to be the best tasting.