Melissa Clark's Seared Broccoli & Potato Soup

Name: Melissa Clark's Seared Broccoli & Potato Soup
Cuisine: American
Ingredients: 1/2 cup olive oil, plus more as needed; 2 pounds (2 heads) broccoli, separated into small florets, stems peeled and diced; 2 1/2 teaspoons kosher salt, more to taste; 2 tablespoons unsalted butter; 1 large Spanish onion, diced; 5 cloves garlic, chopped; 1/2 teaspoon black pepper, more for finishing; 1/4 teaspoon red pepper flakes; 1/2 pound potatoes, peeled, and thinly sliced; 1/4 teaspoon finely grated lemon zest; 1 1/2 tablespoons fresh lemon juice, more to taste; Grated or shaved Parmesan, to finish (optional); Flaky sea salt, to finish