In a large skillet, heat the olive oil and butter over medium heat. Add the thinly sliced onions and a pinch of salt. Cook, stirring occasionally, until the onions are golden brown and caramelized (about 20-25 minutes). If the onions start to stick, add a splash of water to deglaze the pan. Season with pepper to taste and set aside.

Preheat your oven to 350°F (175°C). Place the sourdough slices on a baking sheet and toast them in the oven for about 5-7 minutes, or until they are crispy and lightly browned.

Top each slice of toasted sourdough with a generous amount of caramelized onions. Lay slices of brie cheese over the onions. Sprinkle fresh thyme leaves on top.

Return the assembled toasts to the oven for about 5 minutes, or until the brie is just starting to melt.

Remove the toasts from the oven and drizzle with honey. Serve immediately, garnished with additional fresh thyme if desired.