Preheat oven to 400°F.
Add broccoli florets to a parchment-lined baking sheet. Drizzle with 2 tbsp olive oil, season with ½ teaspoon salt and ¼ teaspoon pepper, and then toss until evenly coated.
Roast for 30 minutes, tossing halfway through, until the broccoli is tender and lightly browned on the edges.
While the broccoli roasts, make the dressing. In a small bowl or jar, whisk together the remaining 2 tablespoons of olive oil, lemon juice, ½ teaspoon salt, ¼ teaspoon pepper, and red chili flakes (if using).
When the broccoli is finished roasting, transfer to a serving bowl or leave in the baking dish. Drizzle with the lemon dressing.
Add chopped walnuts and parmesan cheese, toss to combine, and serve warm.