Place the phyllo shells on a baking sheet lined with parchment paper. Spoon 1 rounded teaspoon of chicken filling into each shell, then add about 1 teaspoon of the egg mixture. Let the shells sit for about a minute so the egg can settle to the bottom. Then add about another teaspoon of egg to each shell, filling it close to the top.
Bake the cups until the custard is set, about 15 minutes. After the cups have cooled, freeze them for up to 2 weeks. To serve, simple reheat them in a 350 oven until heated through, 10 to 15 minutes. Makes 30 quiches.
1. Meanwhile, whisk flour and cornmeal in a shallow dish. Whisk the remaining 1 tablespoon hot sauce and 1 tablespoon vinegar in a small bowl.
2. Remove the chicken from the marinade and roll in the flour mixture until evenly coated. (Discard remaining marinade and flour mixture.) Sprinkle both sides of the chicken with cayenne.
3. Heat 1 tablespoon oil in a large nonstick skillet over medium-high heat. Add half the chicken, placing each in a little oil. Cook until golden brown and cooked through, 3 to 4 minutes per side. Transfer to a serving platter. Repeat with the remaining 1 tablespoon oil and chicken, reducing the heat if necessary. Transfer to the platter. Drizzle the chicken with the reserved hot sauce mixture. Serve with carrots, celery.
The chicken can marinate (Step 1) for up to 1 hour.