In a mixing bowl, combine the softened butter, white miso, grated garlic, chopped herbs, chopped jalapeño (if using), and a pinch of black pepper. Stir until smooth and evenly mixed.
Spread the miso butter evenly on one side of each slice of sourdough bread.
Assemble the sandwiches: place shredded Gouda and shredded Monterey Jack between two buttered slices, buttered sides facing inward.
Heat 1–2 tablespoons of olive oil or butter in a large skillet over medium heat.
Place sandwiches in the skillet and cook until golden brown and the cheese is melted, about 3–5 minutes per side, pressing gently with a spatula and flipping carefully.
Remove from the skillet, drizzle with hot honey to taste, slice, and serve immediately.