Season chicken breasts on both sides with salt and pepper. Heat oil in a large oven-safe skillet over medium-high heat until almost smoking. Place chicken, skin side down, and sear until skin is well browned, 6 to 8 minutes. Turn chicken skin side up and transfer skillet to oven. Bake until the thickest part of the breast registers 160°F, about 15 minutes. Transfer chicken to large platter or individual serving platters and tent with foil.
Place skillet over medium heat, add shallot and cook until softened, stirring frequently. Add flour and cook 1minute, stirring constantly. Add Ale and cook until reduced by half, stirring to scrape browned bits from bottom of pan.
Stir in mustard, chicken broth, cream, thyme,1/4 teaspoon salt and 1/8 teaspoon pepper. Cook until slightly thickened.
Remove from heat and whisk in cheese until melted and smooth. Drizzle about 3 tablespoons sauce over each breast, passing any leftover sauce along side. Serve immediately.