Arrange the duck legs in a single layer in a baking dish. Slide 5 thyme sprigs under each leg and place another 5 sprigs on top of each leg. Cover the baking dish with plastic wrap and refrigerate for 12 to 15 hours.
Preheat the oven to 200 degrees F.
Remove the duck from the baking dish and rinse under cold water to remove the seasonings.
Set the duck legs skin-side-down in a Dutch oven and sprinkle with a few pinches of salt and pepper. Pour in enough rendered fat to fully submerge the legs. Cover and transfer to the oven. Bake until the meat easily falls off the bone, 10 to 12 hours. Allow the duck to cool in the fat; then peel and discard the skin and shred the meat into bite-size pieces.
For the sopes: Heat 1 inch of vegetable oil in a large skillet over medium-high heat. Fry the sopes until golden brown on both sides.
Warm up the shredded duck meat in a little fat in a hot skillet; just add the meat and cook for about 45 seconds, turning it once.
Top each sope with some duck meat. Add a few slices of Brie, working quickly to allow the heat from the duck to soften and melt the cheese a bit. Top with a small dollop of creme fraiche and a little Sriracha, and finish with some microgreens.