Salt the eggplant: Place the cubed eggplant in a colander and toss with 1 teaspoon salt.
Let it sit for 15–20 minutes to draw out moisture and reduce bitterness. Pat dry with paper towels.
Brown the beef: Heat a large skillet over medium-high heat. Add the ground beef and cook, breaking it up, until well browned and crisp around the edges, 6–8 minutes.
Season with a pinch of salt and pepper. Transfer to a bowl, leaving about 1 tablespoon fat in the pan (or add olive oil if needed).
Cook the eggplant: Add 2 tablespoons olive oil to the skillet. Add the eggplant and cook over medium heat, stirring occasionally, until golden and tender, 8–10 minutes.
If the pan looks dry, add another drizzle of oil. Avoid overcrowding so it sears instead of steams.
Soften aromatics: Push eggplant to one side. Add onion to the empty space and cook 2–3 minutes until translucent.
Stir in garlic and cook 30 seconds until fragrant.
Layer in spices: Sprinkle in smoked paprika, oregano, cumin, and red pepper flakes. Stir to coat the eggplant and onion in the spices.
Build the sauce: Add tomato paste and cook for 1 minute to caramelize. Stir in the drained diced tomatoes and beef broth.
Bring to a gentle simmer.
Combine and reduce: Return the browned beef and any juices to the skillet. Stir well and simmer 4–6 minutes, until slightly thickened and glossy. Taste and adjust salt and pepper.
For extra richness, swirl in 1 tablespoon butter.
Finish and serve: Sprinkle with parsley or basil. If using cheese, scatter it over the top, cover for 1–2 minutes to melt, then serve hot.