Panko Crusted Chicken with Chanterelle-Gruyere Sauce

I found these gorgeous golden trumpet like mushrooms at Costco (of all places!) for $8.99 per pound which is very reasonable for this hard to find (at least around here) exotic.  I decided to use them in a lightly cheesy cream sauce and serve the sauce over chicken.  Here's what I did:

Makes 4 servings

 For the chicken:
4 six to eight ounce boneless, skinless chicken breasts, pounded a bit to even
1 cup flour
2 eggs lightly beaten with a few tablespoons water
About 2 cups panko crumbs
salt and pepper
Vegetable oil for pan frying

Begin by heating enough oil in a large skillet to come up about a half an inch.  Get the oil nice and hot while you're breading the chicken.
Season the chicken with salt and pepper.  Set up a breading station and dredge the chicken first in the flour, then the beaten egg and last the panko.
Brown the chicken until golden and then place them in a shallow baking dish. Bake the chicken in a 350F oven for 15 to 20 minutes.

For the sauce:
2 Tbl butter
2 Tbl extra virgin olive oil
1 medium shallot, minced
A pinch of thyme
1 pound Chanterelle mushrooms (or substitute Shitakes)cut in good size chunks
1 tsp instant flour (Wondra) plus more if needed
1/2 tsp salt
1/4 tsp white pepper 
1/4 cup dry white wine
1  1/2 to 2 cups half and half
2 ounces shredded Gruyere cheese

In a large saute pan, heat the oil and butter, add the shallots and saute until the shallots soften. Add the mushrooms and thyme and continue to saute until the mushrooms give off their liquid.  Continue to saute to let the liquid evaporate. Stir in the instant flour.
Add the salt, pepper and wine.  Simmer for about a minute.
Stir in 1  1/2 cups of the half and half, bring up to a simmer and cook to thicken the sauce. If you like a thinner sauce add that extra 1/2 cup of half and half now. Simmer until the sauce lightly coats the back of a spoon. 
Turn off the heat and stir in the cheese.
Ladle a little sauce over the chicken and enjoy!