Start the polenta base. In a medium pot, bring the broth and milk to a gentle simmer over medium heat.
Whisk in the polenta in a slow, steady stream to avoid lumps.
Simmer low and slow. Reduce heat to low. Cook, whisking often for the first 5 minutes, then stirring every few minutes with a wooden spoon. Keep the mixture at a gentle bubble.
Add splashes of hot water or broth if it gets too thick before it softens. Total time: about 30–40 minutes for stone-ground polenta.
Finish the polenta. When creamy and tender, stir in the butter and Parmesan. Season with salt and pepper.
The texture should be loose and spoonable—add a bit more liquid if needed. Cover and keep warm on the lowest heat.
Make the gremolata. In a small bowl, combine parsley, lemon zest, garlic, olive oil, and a pinch of salt. Stir and let it sit so the flavors meld.
This brightness will lift the whole dish.
Sauté the vegetables. Warm olive oil in a large skillet over medium heat. Add shallot and cook 1–2 minutes until soft. Add asparagus and zucchini; cook 3–4 minutes until crisp-tender.
Stir in peas and spinach, plus salt and red pepper flakes. Cook 1–2 minutes more. Finish with lemon zest or a squeeze of juice.
Assemble. Spoon the creamy polenta into shallow bowls.
Top with a generous pile of vegetables. Spoon the gremolata over the top. Finish with extra cheese, black pepper, and a drizzle of olive oil if you like.