Sprinkle zucchini slices with salt and let sit 10 minutes; blot dry.
Preheat grill or skillet over medium-high. Lightly brush zucchini with olive oil and grill 2–3 minutes per side until slight browning; drain on paper towels.
Preheat oven to 375°F (190°C).
In saucepan, brown beef with salt. Drain fat.
Add onion and garlic to pan; sauté until fragrant. Stir in crushed tomatoes, basil, pepper; simmer 30–35 minutes covered.
Mix ricotta, Parmigiano, and egg in a bowl until smooth.
In baking dish, spread ½ cup sauce. Layer zucchini to cover, spread ½ of ricotta mix, top with 1 cup mozzarella. Repeat layers: zucchini, ricotta, mozzarella.
Finish with remaining zucchini and sauce; cover with foil and bake 30 minutes.
Remove foil and bake 20 minutes more; sprinkle with remaining mozzarella and bake until melted, ~10 minutes.
Let rest 5–10 minutes before slicing and serving.