Heat a nonstick 12-inch saute pan over medium heat. Add butter and oil and swirl around the pan until melted. Add the country ham and saute until it begins to brown, about 3 minutes. Turn heat to low. Stir in roasted red peppers and beaten eggs. After the eggs begin to set, stir slowly from edge to edge with a heat-resistant rubber spatula until large curds form. This will take 5 minutes or so. When eggs are still moist and slightly runny, fold in the grated cheese and season with salt and pepper.
Remove the pan from the heat and serve with fried green tomatoes and buttermilk biscuits with sorghum butter.