Heat the olive oil in a large skillet or Dutch oven over medium-high heat until shimmering. Add the ground beef and cook, breaking it apart with a spoon, until it's no longer pink and beginning to brown around the edges, about 4-5 minutes. Add the finely diced onion and continue cooking for another 2-3 minutes, stirring occasionally, until the onion softens slightly and the beef develops a deeper golden color. This browning step is crucial for developing the savory depth of flavor that makes this casserole satisfying.

Reduce heat to medium and sprinkle the garlic powder, paprika, salt, and black pepper directly over the cooked beef and onions. Stir well to distribute the spices evenly, cooking for about 30 seconds to bloom the spices and release their aromatics. Add the Dijon mustard and tomato paste, stirring constantly for 1-2 minutes until the tomato paste darkens slightly and the mixture becomes fragrant. I like using tomato paste this way because it adds deep umami without any dairy, which is essential for this dish to feel rich and complete.

Pour in the beef broth and dairy-free milk, stirring to combine with the spiced beef mixture and ensure no lumps remain in the tomato paste. Bring the liquid to a boil over medium-high heat, then immediately add the uncooked elbow pasta, stirring frequently to prevent sticking. The pasta will release its starches into the liquid as it cooks, creating a creamy, naturally thickened sauce without any dairy. Once it reaches a boil, reduce the heat to medium-low to maintain a gentle simmer rather than a rolling boil, which helps the pasta cook evenly.

Simmer the casserole uncovered for 8-12 minutes, stirring occasionally to prevent the pasta from sticking to the bottom, until the pasta is tender and the liquid has thickened into a sauce-like consistency. The cooking time will depend on your stove and the thickness of the bottom of your pan—start checking at 8 minutes and taste a piece of pasta to determine doneness. Stir in the dried oregano during the final minute of cooking. Taste the finished casserole and adjust seasoning with additional salt and pepper if needed—I find the flavors can shift slightly as everything simmers together, so this final check is important.