In a large skillet, heat olive oil over medium heat. Once pan is hot, add onion, carrots, pepper, and garlic. Lightly salt and sauté for 2-3 minutes until onions are soft and slightly translucent.
Increase heat to medium-high, then add the ground turkey. Use a wooden spoon to stir and break up into smaller pieces while cooking until the meat is lightly brown with no pink visible, about 3-4 minutes.
Add ground paprika and chili powder, then stir to mix the spices well into the ground meat and vegetables.
Add diced tomatoes, tomato paste, red wine vinegar, Worcestershire sauce, water, and brown sugar. Stir gently to combine all ingredients and cook at this heat for 1 minute.
Reduce heat to low-medium and simmer for 20-25 minutes, just until the flavors permeate throughout all of the ingredients and the sauce has slightly thickened.
Meanwhile, halve Hawaiian rolls and place onto a baking sheet. Bake at 350 degrees for approximately 5 minutes, just until lightly toasted.
When the meat mixture is done, scoop heaping spoonfuls onto each roll. Serve immediately.
Notes
Best way to add cheese to Sloppy Joes: place bottom bottom halves of slider rolls onto a baking sheet, top with the cooked meat, then sprinkle on shredded cheese. Place tops of slider rolls on baking sheet. Bake at 350°F just until cheese has melted, about 3-4 minutes.MAKE AHEAD: Make the meat and refrigerate overnight. When you're ready to serve, remove the meat from the refrigerator and heat in a saucepan or microwave before making the sliders and serving.