Heat a Dutch oven or a large, deep 12-inch skillet with a sturdy bottom over medium-low heat. Add the oil onion, carrot, salt, and pepper. Let cook until the onion turns brown and soft, about 10 minutes (don't shortcut this step; it builds a lot of flavor).
Add the garlic and let cook just until fragrant, about 30 seconds.
Increase heat to medium-high and add the ground beef. With the back of a large spoon or a sturdy spatula, break the meat into small pieces. Continue to brown, stirring periodically, until the meat is browned and cooked through, about 6 minutes.
Remove pan from the heat and carefully drain off any excess fat, leaving just a little bit in the pan to keep the meat moist (if you are using meat that is 93% lean, you likely will not need to drain it).
Return the pan to the medium-high heat. Stir in the hot sauce, Dijon, and smoked paprika. Add the beef broth. Scrape up any browned bits stuck to the pan.
Add the water and stir to combine. Bring the liquid to a boil over medium-high heat.
Once the liquid is boiling, add the pasta and cook until al dente according to package instructions, stirring often and scraping a spoon along the bottom of the pan to keep it from sticking. If at any point the pasta becomes to dry, splash in a bit of water.
Remove the pan from the heat and let cool 1 minute. Add the Greek yogurt and cheddar. Stir until the cheese is melted and the ingredients are well combined.
Stir in half of the chives, then sprinkle the remaining chives on top. Enjoy hot.
TO STORE: Refrigerate leftovers in an airtight storage container for up to 3 days.
TO REHEAT: Rewarm Hamburger Helper in a Dutch oven on the stovetop over medium-low heat.
TO FREEZE: Freeze leftovers in an airtight freezer-safe storage container for up to 3 months. Let thaw overnight in the refrigerator before reheating.