Whole Roasted Cauliflower With Cheddar Beer Sauce

Name: Whole Roasted Cauliflower With Cheddar Beer Sauce
Ingredients: 10 cups water; 3 tablespoons kosher salt; 1/3 cup olive oil, plus more for drizzling; 3 tablespoons fresh lemon juice; 2 tablespoons unsalted butter; 1 tablespoon granulated sugar; 2 teaspoons crushed red pepper flakes; 2 teaspoons whole black peppercorns; 1 bay leaf; 1 head of cauliflower, leaves removed; 1 teaspoon smoked paprika; 2 tablespoons butter; 2 tablespoons all-purpose flour; ½ cup whole milk; ¾ cup beer (something light like a pilsner or amber); 2 teaspoons Worcestershire sauce; 2 teaspoons spicy brown mustard; ½ teaspoon salt; ½ teaspoon black pepper; 2 cups sharp cheddar cheese, grated