Melt the butter with the olive oil in a large skillet over medium-high heat. Add the bell peppers and shallots and cook, stirring, until the vegetables are just soft, about 3 minutes. Add the garlic and cook, stirring, for 1 minute. Using a slotted spoon, transfer the vegetables to a large bowl. Add the shrimp to the hot skillet and cook, stirring, for 1 minute. Add the shrimp or chicken stock, scraping the bottom and sides of the skillet, and cook for 30 seconds. Add the cream and bring to a boil. Cook, stirring, until the shrimp are just cooked through, 3 to 4 minutes.

Using a slotted spoon, remove the shrimp and place them in the bowl with the vegetables.

Boil the liquid in the skillet until it is reduced and thick enough to coat the back of a spoon, about 3 minutes. Pour the mixture into the bowl with the vegetables and shrimp. Add the pasta, basil, salt, black pepper, and cayenne. Toss to coat evenly.

Put equal amounts of the pasta mixture in shallow soup bowls and garnish with equal amounts of the pecan pieces and Parmesan cheese.
Serve warm.