In a small pot, cover dried mushrooms with broth or stock and bring to boil; remove from heat, cover and let stand 15 minutes.
Remove mushrooms with a slotted spoon, reserving broth; chop and set aside. Heat a large non-stick or cast iron skillet, over medium-high heat, with 2 tablespoons extra virgin olive oil. Add and cook sausage until browned; crumble; remove from pan to a paper towel-lined plate, leaving enough oil and drippings in pan to coat; set aside.
Add rice to drippings; brown and heat 3 to 4 minutes; remove to a plate or a bowl.
Return pan to heat and add 1 tbsp. extra virgin olive oil.
When hot, melt the butter; when it foams, add mushrooms and brown well.
Add shallots and garlic to mushrooms; season with salt, pepper, thyme and tomatoes.
Add rice and sausage to the dried mushrooms; add marsala and let it absorb for a few minutes.
Add mushroom broth and toss with greens and cheese; 1 to 2 minutes; douse with lemon and serve.