Warm a nonstick skillet over medium heat. Add 1 T brown butter to pan and lightly brown challah slices.
Remove bread from skillet to build sandwich, keeping pan warm. On toasted side of bread (this helps cheeses melt quickly and gives a toasty crunch to both sides of bread), spread mustard, layer cheeses (spread goat cheese under top piece), drizzle with honey, top with onions, then add top piece of bread.
Add remaining 1 T of brown butter to pan and return sandwich to skillet. Cook approx. 3 min per side, being careful not to scorch butter or bread. Serve hot.