Place pancetta in a cold medium sauté pan. Turn heat to low and cook, stirring occasionally, for about 8 to 10 minutes, or until pancetta is lightly browned and fat is rendered.
Add garlic and cook for 2 more minutes or until it starts to brown. Transfer mixture, including rendered fat, to a small heat-proof bowl. Add sun-dried tomatoes and set aside.
Heat oven to 350°F.
Slice top rind off goat brie and place wheels in an ovenproof dish with a 2-inch space between them. Bake until cheese is hot and melted throughout, about 25 minutes.
While brie is baking, bring a large pot of salted water to a boil. Add pasta and cook according to package instructions. Reserve a cup of pasta water, then drain and set aside in a large bowl.
Toss pasta with pancetta, garlic, and sun-dried tomato mixture. Season with salt and pepper.
Remove brie from the oven and immediately cut a slice through the rind of each wheel so melted cheese pools to the center of the dish.
Using tongs, twirl pasta into the cheese, adding enough of the reserved pasta water to keep the sauce creamy. Transfer to a serving dish and garnish with basil.