Prepare Vegetables: Roast tomatoes on baking sheet with foil drizzled with olive oil at 400 until they slightly burst.
Boil broccoli rabe for 5 minutes then place in ice bath, drain, then saute with 2 cloves of shaved garlic, olive oil and a pinch of crushed red pepper.
Saute 2 chopped garlic and 2 chopped shallots in olive oil, add sliced mushrooms and a splash of white wine, cook until moisture evaporates.
For the Polenta: Boil water and broth along with the butter olive oil, whisk in polenta cook until bubbly and creamy.
Stir in grated Parmigiano, herbs and the half and half, drizzling a little more olive oil.
Lay poached eggs on top.