Into a small skillet measure the olive oil and add the garlic. Warm the skillet over medium low heat for 5-10 minutes, stirring occasionally. The garlic should be softened but should not brown. Add the bell pepper and continue to cook for another 2-3 minutes.
Remove skillet from heat. Stir in the lemon juice, mustard, black pepper, salt and parsley.
Place the brie on a rimmed baking sheet. (See my note in Instruction #7 about using a heatproof skillet.) Using a fork, poke holes all over the top surface of the brie. Allow the fork to go all the way to the bottom of the cheese but do not pierce the bottom rind.
Pile the red peppers with garlicky olive oil onto the top surface of the cheese. Use a spatula to scrape every last drip of flavored oil onto the cheese. Set aside for 15 minutes, allowing the garlic oil to drip through the holes you’ve made in the cheese. (You can marinate it in the refrigerator for longer, even overnight. If doing so, cover with plastic wrap before refrigerating).
If using BBQ: Preheat BBQ to 350°F and prepare for indirect grilling. Once BBQ is heated, place the cheese-pan on the grill, being sure that it is over indirect heat (i.e., that the heat is not directly below the pan). Put the cover of the BBQ down. If using oven: Preheat oven to 350°F Once oven is preheated put in the pan of cheese.
Bake/BBQ for 15 minutes. If the brie is bulging at the sides and soft to the touch on top, it’s ready. If it’s not soft and bulging, bake/BBQ for another 5-7 minutes but check on it every minute or so (you want to catch it at the bulging stage not at the oozing-all-over-the-pan stage).
It’s nearly impossible to move the brie onto a serving plate once it’s soft and gooey, therefore I used a 6" cast iron skillet and served directly from it. Place the pan of cheese on top of a heat-proof pot holder or trivet. Warn Guests: Pan is HOT. Serve with slices of French bread and/or water crackers. Red grapes would be a nice addition, too.