Preheat the grill to medium high heat. If you don't have a vegetable basket, spread a sheet of heavy duty foil over half of the grill.
Toss the green pepper, onions, and mushrooms with the olive oil. Season with salt and pepper. Place the vegetables in a grill basket or spread them out over the foil on the grill. Add the brats directly to the grill grates. Grill with the cover closed for about 6-7 minutes. Check the vegetables. If they're getting browned, flip them over. If the bottoms of the brats are browned, flip them as well. Cover, and continue to grill, checking every few minutes, until the veggies are softened and starting to char and the brats reach an internal temperature of 160 degrees.
For the cheese sauce:
In a medium saucepan over medium heat, melt the butter. Whisk in the flour and cook until thick and fragrant, about a minute. Remove from heat and slowly whisk in milk. Add the cream cheese cubes. Return to heat and bring the mixture to a boil, whisking constantly. Turn the heat to low and stir until cheese is melted and cream cheese is completely smooth. Remove from heat and season to taste with salt and pepper. I usually don't need much salt, but like a lot of fresh cracked pepper in mine!
To serve, place the brats in the buns and top with the grilled veggies and sauce!