Pour vegetable oil into a 10" cast iron skillet (or other cookware). Add two tablespoons shortening. Warm over low heat until sizzling hot 5-7 minutes). While oil is warming, prepare onions and flour mixture.
Peel onion and slice into rings (desired thickness). Set aside.
Pour buttermilk into a medium bowl. Set aside.
Combine flour, salt and black pepper in a medium bowl. Set aside.
Dip onion ring in buttermilk. Dredge in flour. Place on a large plate.
Repeat until all onion rings are coated.
Drop several onion rings into skillet with hot oil. Arrange in a single layer. Fry 2-3 minutes on one side. Flip and repeat until golden brown. Drain on paper towels.
Before adding second layer of onion rings, drain hot oil (leave crumbs in skillet) into a heatproof container or another skillet. Discard crumbs. This step is necessary to prevent burnt crumbs which will alter taste of onion rings.
Return oil to 10" skillet. Heat for 2-3 minutes over medium heat BEFORE frying remaining onion rings. Repeat previous steps.