In a large skillet, heat olive oil over medium-high. Add broccoli, trimmed and cut into florets, and cook until broccoli begins to brown, 4 minutes. Add garlic and cook, stirring occasionally, until broccoli is crisp and tender and garlic begins to brown, 3 minutes.
Add red pepper flakes, season with salt and pepper, and transfer to serving bowl. Toss with lemon zest, lemon juice, parmesan, and walnuts. Serve warm or at room temperature.