In a 12-inch oven-safe skillet, heat the oil over medium-high heat. Cook the onion and carrot until soft for 3 minutes, stirring frequently.
Add the ground beef, breaking the meat apart with a spatula, and cook, undisturbed for 30 seconds. Make a small room, add garlic and cook until fragrant. Add 1 teaspoon salt and ¼ teaspoon black pepper, continue cooking and stirring until the meat is browned for about 4 minutes.
Add the flour and tomato paste, cook for 1 minute, stirring frequently. Pour in the red wine. Gently scrape up the brown bits from the bottom of the pan and continue cooking until the liquid is almost gone, stirring frequently.
Add the Worcestershire sauce, thyme, rosemary, and broth. Bring to a boil, reduce the heat to low then simmer, uncovered, for about 10 minutes or until the sauce is thickened to a gravy-like consistency, stirring occasionally. Taste, add more salt or Worcestershire sauce if necessary. Turn off the heat.
Stir in the peas and corn. Mix well until combined.
Preheat the oven to 400°F.