Heat oil over medium heat in a large high-sided pan with a lid. Add garlic and cook until fragrant, about 1 minute. Add broccoli, cauliflower, and lemon-pepper; mix well. Cover and cook for 4 minutes. Remove lid, mix well, and pour in chicken broth. Replace lid and let the broth steam cook the vegetables for about 4 minutes.
Meanwhile, bring a large pot of lightly salted water to a boil. Cook gnocchi in the boiling water until they float to the top, 3 to 5 minutes. Drain, reserving 1/2 cup of cooking water to mix into the sauce.
Pour lemon juice over the vegetables and mix to combine. Pour in cream and capers. Simmer for about 6 minutes. Add gnocchi and pasta water. Season with salt and pepper. Top with Parmesan cheese and let sit for 2 minutes before serving.