If you like meatloaf, you'll love these personal meatloaf patties!
In a medium bowl, combine the chutney, 1 tablespoon EVOO and 1 teaspoon mustard; season with salt and pepper. Add the carrots and toss.
Place the beef in a large bowl. Set aside the 4 largest slices of bread for toast. Using a food processor, grind enough of the remaining bread to get 2 cups crumbs. Add the crumbs to the beef. Coarsely chop the stewed tomatoes in the food processor; remove 1/2 cup and add to the beef. Stir the egg and remaining 1 tablespoon mustard into the beef; season with salt and pepper. Shape into four 4-inch-diameter patties.
Puree the remaining tomatoes, then transfer to a small saucepan. Cook over medium heat, stirring now and then, until thickened to 1/2 cup, about 5 minutes. Meanwhile, toast the 4 slices of bread.
In a large nonstick skillet with a lid, heat the remaining 2 tablespoons EVOO over medium to medium-high heat. Add the patties and cook, turning once, until browned, about 5 minutes. Lower the heat to low, spoon half of the tomato sauce over the patties, cover with the lid and cook the patties until cooked through, about 3 minutes.
On serving plates, top the toast with some of the remaining tomato sauce, the burgers, more sauce and the arugula; serve with the carrot salad.