Prepare the chiles: Preheat the oven to 400°F. Cut slit in end of each poblano to allow release of steam during cooking. Brush chiles with oil and roast in oven until skins are lightly charred and blistered, 5 to 10 minutes. (Leave oven on.) Place poblanos in a plastic bag and seal. Let them steam 5 minutes; using small knife, carefully peel off skin. Slit each chile open from top to bottom (leaving ends intact) and remove seeds.
Meanwhile, in a pot of boiling salted water, cook potatoes until just tender. Drain and place in a bowl. Mash with a fork. Mix in goat cheese and season to taste with salt and black pepper. Stuff chiles with this mixture and arrange in a single layer in a baking dish.
Make the sauce: In a skillet, heat oil. Add red chiles, scallions, and garlic and cook until softened, about 2 minutes. Add tomatoes, tortillas, brown sugar, and oregano, and cook over gentle heat for 10 minutes. Pour into a blender and blitz to almost smooth but slightly textured sauce. Pour sauce over stuffed chiles and bake for 10 to 15 minutes.
Sprinkle top with Cheddar. Dollop sour cream on top and serve.