Position the oven rack to the middle position and preheat the oven to 375 degrees F. Line a baking sheet with parchment.
Put the cranberries, ketchup, honey, sriracha, 1/2 cup water and 1/2 teaspoon of the mustard in a small saucepan and stir to combine. Heat over medium-high heat until the mixture starts to bubble, then reduce to a simmer and cook, stirring occasionally, until the mixture thickens and the cranberries soften, about 10 minutes. Use a potato masher to crush the cranberries until mostly smooth. Add the rosemary and 1/4 teaspoon salt and set aside to cool slightly.
Grate the carrot and onion on the small shredding side of a box grater into a large bowl. (This will save any onion liquid, which will help keep the meatloaf moist.) Add the beef, turkey, egg, barley, Worcestershire, remaining 2 teaspoons of the mustard, 1 teaspoon salt and several grinds of pepper. Use your hands to mix everything together until well combined.
Transfer the mixture to the prepared baking sheet and shape into a 9-by-4-inch loaf using your hands. Brush the meatloaf on all sides with half of the cranberry glaze. Bake until the glaze starts to adhere and dry slightly, about 15 minutes. Brush the meatloaf on all sides with the remaining glaze and bake until a thermometer inserted into the center of the meatloaf registers 155 degrees F, 30 to 35 minutes. Garnish with rosemary sprigs before serving.
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