In a 10” non-stick skillet, heat 1/4 cup olive oil over moderate heat. Add the onion with salt and pepper to the skillet, cook, stirring occasionally, until softened, 2 - 3 minutes. Remove from heat.
Peel potatoes and coarsely grate in food processor. Squeeze potatoes with paper towels to remove excess moisture and place in a bowl. Add onion mixture, stirring to coat potatoes and stir in cheese with 1 ounce Cholula Chili Garlic.
Heat 2 tablespoons olive oil in the same skillet over moderate heat. Add potato mixture, then press firmly into a cake and round edges with a spatula. Cover skillet and cook potato cake until underside is crusty, 8 - 10 minutes. Slide onto a plate. Flip potato cake into the skillet again to cook other side. Cover and cook until potatoes are tender and underside is crusty, about 10 minutes.
Top with parsley, a bit more Parmesan cheese and a few shakes of Cholula Chili Garlic to taste. Slide cake onto a platter and cut into desired serving sizes.