Preheat your oven to 350°F (175°C). Place the unsliced loaf of sourdough on a cutting board and make deep cuts in a grid pattern, leaving about half an inch intact at the bottom.
Thinly slice the Monterey Jack cheese. Freshly sliced cheese fits better into the cuts of the bread.
In a mixing bowl, combine the melted butter, finely diced green onions, and poppy seeds. Stir well to distribute the ingredients.
Stuff the cheese slices into the cuts of the bread, ensuring to pack it in as much as possible.
Brush the bread generously with the butter mixture, making sure to coat all the crevices.
Wrap the bread in aluminum foil and place it on a baking sheet. Bake for about 20 minutes.
After 20 minutes, carefully unwrap the foil and return the bread to the oven for an additional 10-15 minutes until golden and crispy.
Remove from the oven, let it cool for a minute, and serve warm for dipping.