Put a large, heat-proof serving dish in the preheated oven.
Rinse the dried mushrooms in a large bowl of cold water. Mix around to get rid of grit and sand. Rinse a few times, letting the dirt settle to the
bottom of the bowl. Transfer the clean mushrooms to a microwave-safe bowl. Add the chicken broth to the mushrooms and microwave for 1 minute until
broth is steaming hot. Let stand for 10 minutes. Chop the mushrooms and reserve the broth. Strain the broth through a coffee filter into a bowl with
chopped porcini mushrooms.
Combine the flour, salt, and pepper in a shallow dish. Dredge the chicken pieces in the seasoned flour. Rest in the plate.
Heat 1 T. oil in a 12-inch skillet over medium-highheat until smoking. Place 4 cutlets in the skillet and cook until browned, about 2 minutes. Flip and continue to cook until second sides are opaque, about 30 seconds. Transfer to a clean plate. Add another 1 T. of oil to the skillet and cook the remaining cutlets. Tent loosely with foil.
Add remaining 1 T. of oil to the empty skillet and return pan to medium heat. Add shallots and cook, stirring for 30 seconds. Add 1 tsp. of the seasoned flour and cook, whisking constantly, 30 seconds. Increase heat to medium-high, add vermouth, soaked porcini with the chicken broth, tomato powder or paste, soy sauce, and sugar. Simmer, scaping up the bits, until the sauce is reduced to about 1 cup. This may take 5 minutes.
Transfer the cutlets and any accumulated juices to the skillet. Add thyme and lemon juice. Cover and simmer until cutlets are just cooked through. Adjust seasoning with salt and pepper. Spoon sauce over chicken on the warm serving dish.