Preheat your oven to 350°F and line a baking sheet with parchment paper. While the oven heats up, cut your brie into small, even cubes about half an inch in size. I like to let the brie sit at room temperature for a few minutes first, since it slices more cleanly and melts more evenly once it's in the oven.
Place the mini phyllo shells directly onto your prepared baking sheet, leaving a little space between each one. If they've been sitting in the freezer, give them a few minutes to thaw on the counter first. I find working quickly here helps, since the delicate shells can turn crumbly if handled too much.
Drop a small spoonful of preserves into the bottom of each shell, then add a cube of brie on top. Finish with a few pieces of chopped pecans pressed gently into the cheese. I try to keep my portions consistent so every cup bakes at the same rate.
Slide the tray into the oven and bake for 10 to 12 minutes, just until the brie turns soft and glossy and the shells are golden at the edges. Keep an eye on them near the end, since phyllo can go from perfectly toasted to too brown rather quickly.
Pull the tray out and let the cups rest for a minute or two before drizzling warm honey over the top. Finish with a scatter of fresh thyme leaves for color and a light herbal note, then move them straight to your serving platter while they're still warm.