Preheat a gas or charcoal grill, or a stovetop grill pan, over high heat.
Grill the jalapenos until browned or blistered on all sides and slightly softened, 3 to 5 minutes. Remove from the heat and set aside to cool.
Meanwhile, mix the cheese and oregano in a small bowl. Season with some salt and pepper.
To remove the seeds from the jalapenos, make a crosswise cut at the stem-end of the jalapeno and then slice lengthwise down the middle, being careful not to cut the jalapeno completely in half. Peel open the sides of the jalapeno and, using a spoon, gently scrape out the seeds and veins. Fill the cavities with 1 tablespoon of the cheese-oregano mixture. Then wrap 1 slice of bacon tightly around the stuffed jalapeno to seal in the cheese. Transfer to the hot grill (try to place the jalapeno on the grill on the side where the bacon ends). Grill until the bacon is crisp and fully cooked, 5 minutes. Serve immediately.