Mix eggs, Tabasco, onion, and garlic in a large bowl or baking dish. Add chicken and toss well too coat. Cover and refrigerate for at least 1 hour or overnight.
Preheat oven to 450°F Place a rimmed baking sheet on center rack.
Whisk flour, cornmeal, salt, paprika, and cayenne in a medium bowl. Remove chicken from marinade and roll each piece in flour mixture, shaking off excess. Discard marinade.
Place chicken on preheated baking sheet, and bake for 20 minutes. Lightly brush top of each piece with oil and bake, brushing tops every 10 minutes until chicken is dark golden brown (30 - 40 minutes more).
Transfer chicken to a wire rack and allow to cool slightly. Serve.