Preheat the oven to 375 degrees F. Pulse the bread in a food processor until finely ground; transfer to a large bowl. Add the onion and carrot to the food processor and pulse until finely chopped. Transfer to the bowl with the bread and add the turkey, beef, egg and 1/2 teaspoon each curry powder, salt and pepper. Mix by hand until just combined. Shape into 4 small oblong meatloaves on a foil-lined rimmed baking sheet. Mix the ketchup and chutney in a small bowl and brush over the meatloaves. Bake until just cooked through, about 20 minutes.
Meanwhile, bring a pot of salted water to a boil. Add the potatoes and cook 4 minutes, then add the broccoli florets and stem; cook until the vegetables are just tender, about 6 more minutes. Drain; return to the pot. Toss with the olive oil and the remaining 1/8 teaspoon curry powder. Season with salt and pepper. Serve with the meatloaves.