Preheat oven to 400°F.  (Use convection if you have it)

Place tomatoes on one baking sheet and place mushrooms on other baking sheet. Drizzle 1 Tablespoon of olive oil over tomatoes and 2 Tablespoons olive oil over mushrooms.  Place smashed garlic cloves, 2 sprigs of rosemary and 2 sprigs of thyme on baking sheet with mushrooms.  Toss to combine.  

Remove the thyme leaves from the additional sprigs of thyme and set aside.

Place mushrooms on bottom rack and tomatoes on middle rack.  Roast for 30 minutes.  

Remove tomatoes (they should be soft and starting to turn brown).  Move mushrooms to top shelf and continue to roast for 5 minutes or until crispy (watch during this part so you do not burn the mushrooms).

Remove the mushrooms from the oven.  Cool slightly and sprinkle with 1/4 salt.  

While the tomatoes and mushrooms are roasting, place the water into a medium sized sauce pan and bring to a boil.  Add polenta slowly while stirring, to avoid clumping.  Turn heat down and simmer for 15 minutes until thick and smooth, stirring frequently.

Turn off heat.  Add butter and stir until creamy.  Break goat cheese into several pieces.  Add to polenta and stir until incorporated.  Stir in salt. Taste and adjust salt as necessary.

Scoop the polenta onto 4 plates.  Top polenta with equal portions of the roasted tomatoes and the crispy mushrooms.  Sprinkle the remaining thyme leaves over the plates.  Drizzle one teaspoon of balsamic vinegar over each plate. Serve while warm.