Cook the pasta in a pot of rapidly boiling water. When the pasta is al dente, drain it in a colander reserving ¼ cup of the pasta water.
Oil the grids and preheat the grill to medium-high.
While the grill is preheating, slice the peppers and onion into quarters. Skewer the shrimp to make them easier to cook, and less likely to fall between the grids.
Grill the shrimp until the flesh is bright pink and opaque all the way through. Grill the onions and peppers until they’re tender-crisp and have some lovely grill charring.
When the veggies are done, slice them into strips or bite sized pieces and set aside.
In a pot, melt the butter over medium high heat. Add the shallots, sautéing them until tender. Add the garlic, wait another minute or so, then add the heavy cream. Reduce the heat and allow the cream to come to a simmer, allowing it to reduce for about 5 minutes while you stir constantly. Remove it from heat.
Return the pasta to the pot, along with the shrimp (remove from skewers) and the vegetables. Add the reserved water, and turn the heat to medium-high. Add the butter and cream mixture and just over half of the parmesan. Toss them all together to combine thoroughly. Season with salt and pepper.
Serve immediately sprinkled with the remaining parmesan cheese.
*Do not rinse the pasta. This will prevent the sauce from sticking to it.
**Do not put oil in the pasta water when boiling, this will also prevent the sauce from sticking to the pasta.
***Use real parmesan cheese for this recipe, the hard pellet stuff you get in the cans will not melt properly. You can substitute a preferred cheese instead of parmesan, it is expensive.