Preheat the oven to 350°F (177°C). Line a baking sheet with foil for easy cleanup.
Set the loaf on a cutting board. Using a serrated knife, cut the bread in a crosshatch pattern (about 1-inch apart), making diagonal cuts in both directions. Do not cut all the way through—leave the bottom intact so the loaf holds together.
In a small bowl, stir together the melted butter, minced garlic, parsley, chives, oregano, salt, and black pepper.
Drizzle or brush the butter-herb mixture over the loaf, working it down into the cuts as much as possible.
Stuff the shredded Monterey Jack and pepper jack into all the cuts, distributing it evenly throughout the loaf.
Wrap the loaf loosely in foil and place it on the prepared baking sheet. Bake for 15 minutes.
Open the foil to expose the top of the bread and bake for 10 more minutes, until the cheese is melted and bubbly and the top is lightly golden.
Cool for 5 minutes, then serve warm. Pull apart and enjoy while the cheese is stretchy.