Preheat the oven to 400F.
Slice both ends off the shallots and peel them. Chop them in half length-wise. Place on a baking sheet lined with aluminum foil and drizzle with olive oil before seasoning with salt and pepper.
Roast 20-25 minutes, or until tender and browned. Cut away any tough spots and set aside to cool.
Reduce the oven temperature to 350F.
In a small saucepan over a medium-low heat, melt the butter and add the garlic. Once fragrant, add the balsamic vinegar, honey, and thyme and sauté until syrupy, about 3-5 minutes. Remove from the heat. Add shallots and toss until they are evenly coated in the mixture.
Transfer the shallots to a non-stick 8-inch round cake tin.
In a small bowl, combine the shredded cheeses.
Cut the puff pastry sheets into 2 circles the same diameter as the cake tin. Place one on top of the shallots. Cover with the cheese mixture. Top with the remaining puff pastry sheet.
Bake the tart for 25-30 minutes, and allow to cool at least 10 minutes before turning it out onto a plate to serve.