1Heat the olive oil in a large heavy-bottomed skillet over medium heat. Add the carrots, garlic, and a hefty pinch of kosher salt. Cook, stirring often, until the carrots are tender and the garlic is fragrant.
2Add the ground beef along with another hefty pinch of salt. Break the meat into very small crumbles with a wooden spoon or spatula as it cooks.
3Once the beef is browned and cooked through, carefully drain or blot away any excess grease.
4Stir in the marinara sauce and brown sugar. Reduce the heat to low and let the mixture simmer.
5Turn the broiler on. Arrange the buns cut-side up on a baking sheet. Drizzle the cut sides generously with olive oil and sprinkle evenly with the garlic salt. Broil until golden brown and crisp.
6Spoon the Italian sloppy joe mixture onto the bottom buns.
7Top each with torn burrata, a pinch of flaky salt, freshly cracked black pepper, and the sliced basil. Finish with the top buns and serve immediately.