In saucepan, heat 1 tbsp (15 mL) of the oil over medium heat; cook onion, carrot, garlic, oregano, salt and pepper until softened, 5 minutes. Add tomatoes, breaking up with spoon; add tomato paste. Bring to boil; reduce heat and simmer until thick enough to mound on spoon, 20 minutes.
CHICKEN: Meanwhile, between 2 sheets of plastic wrap, pound chicken to 1/4-inch (5 mm) thickness; cut in half crosswise. Place flour in shallow dish. In separate shallow dish, whisk egg with 2 tbsp (25 mL) water. In third shallow dish, stir together bread crumbs, Parmesan cheese, oregano, cayenne pepper and salt. Dip chicken, turning to coat, into flour, then egg mixture, then bread-crumb mixture.
In large skillet, heat remaining oil over medium-high heat; cook chicken, in batches, turning once, until golden brown and no longer pink inside, 4 to 6 minutes.
Spread 1 cup (250 mL) of the sauce in 13- x 9-inch (3 L) glass baking dish. Arrange chicken, overlapping, over sauce. Pour remaining sauce over top. (Make-ahead: Refrigerate until cold. Cover with plastic wrap and overwrap with heavy-duty foil; freeze for up to 2 weeks. Thaw in refrigerator for 48 hours. Cover with foil and bake in 375°F/190°C oven for 30 minutes. Uncover and continue with recipe.).
Sprinkle with artichokes, then mozzarella; bake in 375°F (190°C) oven until bubbly, about 20 minutes.