Step 1
Bring 1 cup water to a boil. Add dried mushrooms cover and let stand about 20 minutes. Squeeze dry; strain liquid (a coffee filter is handy for this) and reserve.
Step 2
In a food processor mince garlic and rehydrated mushrooms. Add fresh mushrooms and thyme; continue to process until all is minced.
Step 3
Heat oil in a 12-inch skillet over medium-high heat. Add mushroom mixture; saute until nearly all moisture has evaporated 5 to 7 minutes. Turn off heat stir in cheese and season with salt and pepper. Set aside.
Step 4
Mix honey and vinegar in a small bowl.
Step 5
Adjust oven rack to lowest position and heat oven to 425 degrees.
Step 6
Set breasts skin side down on a large heavy lipped cookie sheet. Brush with half of the honey-vinegar; generously salt and pepper. Turn breasts over. Push fingers under skin to make a pocket; stuff with mushroom mixture. Again brush with honey-vinegar and season with salt and pepper. Being careful not to crowd arrange breasts on cookie sheet so thickest ends point outward. (Can now be covered and refrigerated overnight; return to room temperature before roasting.)
Step 7
Roast until golden brown adding water if necessary to keep pan drippings from burning until a meat thermometer registers 160 degrees in the thickest portion of the largest piece 30 to 45 minutes. Transfer chicken to a platter.
Step 8
Scrape pan juices into a medium saucepan. Add reserved mushroom-soaking liquid and enough water to equal 1 1/2 cups of liquid. Bring to a simmer. Add cornstarch mixture; continue to simmer until it thickens a bit.
Step 9
Arrange a breast on each of 8 plates; drizzle with sauce and serve.