Preheat your oven to 400°F and line two large sheet pans with parchment paper. I use parchment because cleanup matters when you're hosting, and hot oil on bare metal sticks terribly. Get the pans in there while the oven heats so they're genuinely hot when vegetables hit them.
Combine the olive oil, smoked paprika, cumin, salt, and black pepper in a small bowl and whisk together. This first mixture is your flavor anchor—it goes directly on the vegetables before roasting. Don't skip whisking because the paprika needs to distribute evenly, otherwise you'll bite into a pocket of pure spice.
Toss all the vegetables (zucchini, peppers, eggplant, cherry tomatoes, and rosemary sprigs) with the oil mixture in a large bowl until everything glistens with coating. I use my hands because it's faster and you can feel when every piece has been touched by the seasoning. This is where most people rush—take 90 seconds to actually coat everything.
Divide the vegetables between the two hot sheet pans and spread them into a single layer, avoiding overlap. Here's my confession: I used to crowd everything onto one pan and wondered why half my vegetables steamed instead of caramelized. Roast for 18-20 minutes, stirring halfway through, until the edges of the zucchini and eggplant turn golden and slightly charred. The cherry tomatoes should start to wrinkle.
Remove the pans from the oven and immediately scatter the minced garlic and lemon zest across the hot vegetables while everything is still steaming. The heat will wake up those ingredients without cooking them past their prime. This is the magic moment—stir everything gently for about 30 seconds so the zest and garlic distribute evenly throughout.
Return the pans to the oven for another 8-10 minutes until the garlic becomes fragrant but not brown. You're looking for that moment where the aroma fills your kitchen but the garlic hasn't started to color. Pull them out and let them rest on the counter for 3-4 minutes before transferring to your serving platter.
Top the warm summer roasted vegetables crowd dish with crumbled feta cheese right before serving, and remove the rosemary sprigs if people prefer. The cheese will soften slightly from the residual heat and create this creamy-salty contrast against the charred vegetables. This final layer is nonnegotiable because it's what actually makes people ask for the recipe.