Preheat the oven to 350 degrees.
If needed, blend the Monterrey Jack and Mozzarella together.
Cut the tops off the peppers. Scoop out the seeds and remove the ribs from the inside. A melon baller turns out to be a good tool for doing this.
Remove the stems and dice the tops of the peppers. Save 1/4 C for the filling.
Place the peppers in a 9x12 baking dish, open end up. You may need to even up the bottoms with a knife so they stand up, but be careful that the bottom is still closed. Add 1/4 C water to dish, cover with damp paper towels and heat on high in your microwave for 2-3 minutes. This will soften the skins but the peppers won't be mushy later.Alternatively, if you want the peppers more done, cover with plastic wrap instead of paper towels. Vent the wrap by poking it with a toothpick several times, and microwave on high for up to ten minutes. In both methods, some liquid may condense in the bottoms of the peppers. Don't drain it out! It has lots of flavor, so leave it in! Brown the meat in a skillet over medium heat in 2 TBSP of olive oil for 8-10 minutes.
Remove the meat to a plate covered with paper towels to drain the excess fat. Scrape the bottom of the skillet to loosen any brown bits that remain--these are the tasty remnants of the Maillard reaction. You can even deglaze the skillet with a dash of red wine if you want to be fancy.
Add another 2TBSP of olive oil to the hot skillet, the onion, garlic, celery, diced peppers, and diced zucchini if using. Simmer on medium heat until softened, about 3-4 minutes.
Add the diced (and drained!) tomatoes, brown sugar, meat, and rice to the skillet. Mix until heated through.
Remove from heat. Add the next five ingredients to the skillet and half of the cheese blend. Mix thoroughly. Let rest for at least five minutes prior to stuffing the peppers.
Stuff the peppers, cover the dish with aluminum foil, and bake for fifteen minutes. The 1/4 C water you added to the bottom of the pan earlier will keep the peppers from sticking and will also help finish steaming the peppers.
Remove the foil and sprinkle the cheese mixture over the tops of the stuffed peppers. Cook uncovered an additional 15 minutes or until cheese is melted.