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