Preheat oven to 400°. Place 1 sheet of thawed phyllo on a flat work surface. Brush with browned butter. Cut the sheet into eighths. At the bottom of each rectangle spoon a line of goat cheese crumble about ½ inch thick, sprinkle with a few thyme leaves and drizzle honey on top. Roll up starting at the bottom, then brush the top with a little more butter. Repeat with remaining ingredients. Place on a rimmed baking sheet lined with parchment.
Bake for 15–20 minutes. Drizzle with a little more honey before serving.