Preheat the oven to 180C / 350F. Lightly oil an appropriately sized oven dish with a little of the olive oil.
Heat a splash of olive oil in a large skillet or pot (preferably with a lid) over medium-high heat. Add the 1 red onion (sliced) and the 1 red pepper (deseeded, stem removed, and sliced into strips). Fry for about 3 minutes, until just starting to soften. Transfer the red onion and red pepper to a bowl and set aside.
In the same pan, add another splash of olive oil and reduce the heat to low. Add the 1 onion (finely chopped) and cook for about 5 minutes, stirring occasionally, until soft.
Add the 2 cloves garlic (crushed), 1 tsp cumin, 1 tsp dried oregano and 4 Tbsp finely chopped chipotle in adobo sauce (or 3 Tbs chilli powder) to the chopped onion. Fry for about 30 seconds, stirring, until fragrant.
Pour in the 250 ml / 1 cup chicken stock and use a spatula to scrape any browned bits from the pan (deglaze). Then add the 2 cups tomato puree (or Italian passata), 1 Tbsp brown sugar, and salt and pepper to taste. Stir and simmer for about 5 minutes, until the sauce thickens slightly.
Nestle the 500 g chicken breasts into the sauce. If you prefer, cut the breasts in half horizontally to reduce cooking time. Cover, reduce the heat to a simmer, and cook until the chicken is cooked through, about 20 minutes.
Remove the chicken from the sauce and set it aside to cool slightly. Take the pan off the heat.
When the sauce has cooled enough to handle, strain it through a fine sieve into a bowl, pressing to extract as much sauce as possible. Reserve ½ cup of the strained enchilada sauce to use in the filling, and keep the remaining strained sauce to pour over the assembled enchiladas later. Return any solids caught in the sieve (onion bits, etc.) to the pan.
Return the reserved fried red onion and red pepper (from step 2) to the pan with the sieve solids. Cut or shred the cooled chicken into bite-size pieces and add it to the pan with the vegetables. Add the reserved ½ cup of strained enchilada sauce and stir to combine. Taste and adjust salt and pepper if needed.
Lay out the 8 tortillas. Divide the chicken-and-vegetable filling evenly among the tortillas (about 1/8 of the filling per tortilla). Roll each tortilla up and place them seam-side down, snugly, in the oiled oven dish.
Pour the remaining strained enchilada sauce evenly over the rolled tortillas. Sprinkle the 1 cup grated Cheddar and the 1 cup grated mozzarella evenly over the top.
Cover the dish with foil and bake at 180C / 350F for 15 minutes. Remove the foil and bake for a further 10–15 minutes, until the cheese is bubbling and golden brown.
Remove from the oven and let rest for a few minutes before serving.