Add everything but the brie cheese to a small skillet and heat to medium-high. Cook, stirring occasionally, until mixture has thickened, pears have softened, and everything appears sticky, about 5 to 8 minutes.
Preheat the oven to 350 degrees F.
Unwrap the brie cheese and use a sharp knife to cut off the top rind (note you can also leave the rind on...either way works). Place cheese in an oven-safe dish (preferably the dish you'll be using for serving). Top with the pear-walnut mixture and bake on the center rack of the oven for 15 to 20 minutes.
Serve baked brie with choice of gluten-free crackers, sliced pears or apples, and/or toasted baguette.
Notes
*Consider goat or sheep's milk brie for those who are allergic to cow's milk