To a large, 12-inch (30 cm) sauce pan add the oil and butter over medium heat. When the butter is melted and bubbly add the pancetta and mushrooms. Cook stirring often until they have reduced and in size and cooked down a little, about 5 minutes.
Add the shallot and more oil if needed and stir well cooking for a further 2 minutes. Add the garlic, basil, rosemary, half of the salt and pepper and tomato paste, mix well. Cook until any liquid is gone.
Add the wine and simmer until the mushrooms have absorbed most of the wine. Stir in the vegetable stock and simmer until most of the liquid is absorbed. Test for salt and add the rest or season accordingly, this will depend on how salty your stock is.
While the mushrooms cook, make the polenta.

In a medium saucepan, heat the chicken stock and salt (taste your stock, if it is salty, adjust the salt amount, remember you are also adding salty cheese) bring to a simmer. Add the yellow cornmeal while whisking until combined and there are no lumps.
Cook at a very low simmer whisking until smooth and thickened. If the polenta thickens too soon, add a little more stock or water. Stir in the Parmesan cheese.