Preheat your oven to 350°F. While it heats, dice the onion into 1/4-inch pieces, mince the garlic cloves, and finely chop the fresh parsley. Shred the cheddar cheese freshly (this melts much better than pre-shredded varieties). Having everything prepped before you start cooking ensures the beef won't overcook while you're chopping.
In a large skillet over medium-high heat, cook the ground beef, breaking it apart as it browns, until no pink remains (about 5-7 minutes). Once browned, drain off excess fat by tilting the pan and spooning it out—this prevents the filling from becoming greasy. Add the diced onion and minced garlic to the meat, stirring constantly for about 2 minutes until fragrant and the onion begins to soften.
Stir in the beef base, water, ketchup, Worcestershire sauce, dried thyme, salt, and black pepper. Bring the mixture to a gentle simmer and let it cook for 5-10 minutes, allowing the flavors to meld together and the sauce to thicken slightly. I like to taste and adjust the seasoning at this point—the beef base and Worcestershire are salty, so go easy on additional salt until you've tasted it.
Stir in the frozen mixed vegetables and the chopped fresh parsley into the beef mixture from Step 3. Cook for just 1-2 minutes, stirring gently—the vegetables will finish cooking in the oven, so you only want to heat them through. Transfer the entire beef and vegetable mixture to a 9x13-inch baking dish or similar-sized ovenproof dish, spreading it into an even layer.
Distribute the gnocchi evenly over the beef filling, pressing down gently so the pieces nestle into the sauce—this prevents them from drying out during baking. Evenly distribute the freshly shredded cheddar cheese over the top, making sure to cover all the gnocchi. I recommend freshly shredded cheese here because it melts into a smooth, creamy layer, whereas pre-shredded cheese contains anti-caking agents that can make the topping grainy.
Cover the baking dish tightly with aluminum foil and place it in the preheated 350°F oven. Bake for 15 minutes covered to allow the gnocchi to cook through and the filling to heat evenly. Remove the foil and continue baking for another 10 minutes uncovered until the cheese is melted and begins to brown slightly on top (you want a light golden color, not dark brown). Let the dish rest for 2-3 minutes before serving—this allows the filling to set slightly and makes it easier to portion.