Heat a gas, charcoal, or wood-fired grill to high.
If using a charcoal or wood-fired grill, place unhusked corn directly in the fire or coals and let cook, turning occasionally, until husks begin to char and kernels are caramelized in most places, about 10-12 minutes. Otherwise, husk corn and place on grill grates. Grill, turning ears as they color, until kernels are deeply golden on all sides, about 10 to 12 minutes. Alternatively, preheat broiler to high and broil husked corn until golden. Transfer corn to a cutting board and let sit until cool enough to handle.
Place pancetta in a medium skillet over medium-high heat. Cook, stirring occasionally, until fat has rendered and pancetta is crisp, about 5 minutes. Remove pancetta with a slotted spoon to a paper towel-lined plate.
Place baguette on grill and grill, flipping once, until charred on the edges but still soft in the center, about 1-2 minutes per side. Rub whole garlic clove on the cut side of both halves, generously brush with olive oil, and season with salt.
Using a large chef’s knife, remove corn kernels from ears. Transfer kernels to a bowl. Dress with olive oil, lemon zest and juice, and red pepper flakes. Add reserved pancetta, Parmesan, basil, and parsley. Toss to combine, season to taste with salt, pepper, and additional red pepper flakes, and transfer to a serving plate. Tear burrata into large pieces and place on corn. Drizzle with olive oil, top with basil and parsley leaves, and serve with grilled garlic baguette.
