First, cut up the pepper jack cheese into bite-sized cubes.
Fill two shallow bowls, one with the flour and one with the panko + oregano. Fill a small bowl with the eggs, and whisk to combine. Dip each cube of cheese in the flour, then the egg, and then the bread crumbs. Try to fully coat each cube as you work. Place the finished cubes on a baking sheet or clean plate.
Once you have coated all the cubes, pop them in the freezer for 5-8 minutes.
These are the fried version. Fill a heavy-duty pot with 2-3 inches of oil (canola or vegetable works well). Heat to around 350°F. Fry each cube for about 20-30 seconds, just until golden brown and crispy- looking. Then remove to a plate lined with paper towels to soak up excess oil. I like to work with metal tongs when frying, as they make it easier to move food but keep my arms away from the hot oil.
If you want a baked version instead-Preheat your oven to 350°F. Pop these in the oven (be sure your baking sheet is lined with parchment paper or a Silpat mat) for 8-10 minutes, just until they begin to melt.