Preheat oven to 350F

In a saute pan, heat the butter and oil and saute the pepper and shallots for 2 minutes

Add the chopped mushrooms and continue to saute until the mushrooms begin to soften

Season to taste with salt and pepper

Layer half the sole fillets in a lightly oiled, low-sided bak- ing dish

Cover with the pepper, shallots, and mushrooms

Place slices of tomato over all

Layer the remaining sole fillets on top and cover with foil

Bake for 15 minutes

Meanwhile, combine the pesto with enough cream to make a thick pourable sauce

Cover the sole with the pesto sauce, return to the oven, and bake uncovered until the sauce is bubbly, about 5 minutes

Serve hot

Serves 4.