Heat the olive oil in a large, heavy-bottomed pot or Dutch oven over medium heat. Add the diced onion and ground beef. Cook, breaking the beef into small pieces, until the beef is mostly browned and the onion has softened.
About halfway through cooking the beef, add the garlic powder, paprika, chili powder, turmeric, salt, and black pepper. Stir well so the seasonings coat the beef and onions.
Add the Dijon mustard and tomato paste to the pot and stir everything together, cooking for about 2 minutes.
Stir in the finely grated zucchini. Cook for 1–2 minutes, stirring frequently, until the zucchini begins to soften and blend into the beef mixture.
(Do not squeeze the zucchini dry. The moisture from the zucchini helps create the sauce and cook the pasta.)
Pour in the chicken broth and stir to combine. Increase the heat and bring the mixture to a boil.
Add in the uncooked pasta and stir well, making sure that the pasta is mostly submerged in the liquid.
Return the pot to a boil, then reduce the heat to a gentle simmer. Cover and cook for 12–14 minutes, or until the pasta is tender.
Stir every few minutes while the pasta cooks, making sure nothing is sticking to the bottom of the pot. If the pasta needs more time but the pot looks dry, add a small splash of additional broth or water.
Once the pasta is tender, remove the pot from the heat and uncover. Stir in the shredded sharp cheddar until completely melted and incorporated into the sauce.
Let it sit uncovered for 2–3 minutes before serving. The sauce will thicken slightly as it rests.
Serve warm with an extra sprinkle of freshly shredded cheddar if desired.