In a small saucepan, bring broth to a boil. Add dried porcini, remove from heat, and let stand until soft, about 15 minutes. Lift porcini from broth, squeezing out any extra liquid, and chop finely. Strain broth.
In a large frying pan over medium heat, stir bacon often until fat is rendered. Add shallots; stir over medium-high heat until bacon begins to brown, about 5 minutes. With a slotted spoon, transfer shallots and bacon to paper towels. If pan is dry, add about 1/2 tbsp. olive oil. Add fresh mushrooms and chopped porcini; stir often over high heat until liquid has evaporated and mushrooms begin to brown, 12 minutes.
Meanwhile, preheat oven to 375°. Sprinkle chicken on both sides with salt and cracked pepper. Heat butter and 1 tbsp. olive oil in a large, ovenproof frying pan over medium-high heat. Add chicken, skin side down, and cook until well browned on the bottom, 5 to 7 minutes. Turn chicken and transfer pan to oven. Bake just until chicken is no longer pink in center of thickest part, about 20 minutes.
Set chicken on a platter and keep warm. Pour wine into pan and bring to a boil over high heat, stirring to scrape up browned bits. Pour mixture into pan with mushrooms and add porcini-soaking liquid, bacon-shallot mixture, and chopped thyme. Stir often over high heat until almost all liquid has evaporated, 8 to 10 minutes. Add salt and pepper to taste. Mound ragout on plates, top with chicken, and garnish with thyme sprigs.
Note: Nutritional analysis is per serving.