In a large skillet over high heat, add the olive oil. Once hot, add the sausage and onion. Brown and crumble the sausage, taking care to caramelize the meat for maximum flavor. Season with 1 teaspoon of salt and ½ teaspoon of pepper, or to taste.
Transfer the browned sausage and onion to the slow cooker. Add the remaining ingredients listed under "Add First". Stir everything together and press it down into an even layer. Cover with the lid.
Cook on high for 2-4 hours or on low for 4-6 hours, until the potatoes are tender. Once done, gently stir the mixture. Taste and adjust the seasoning with more salt and pepper if needed.
Sprinkle the freshly grated cheese over the top in an even layer. Cover with the lid again and let the cheese melt, about 5-10 minutes.
Serve hot with optional toppings like fresh cilantro and sour cream.
