Arrange a rack in the middle of the oven. Place a rimmed baking sheet on the rack and heat the oven to 425ºF.

Cut the stalks off 1 ½ pounds broccoli. Trim off the dried ends, then peel the stalks until you reach the smooth inner flesh. Halve the stems lengthwise, then cut crosswise into 1-inch pieces. Cut the florets into 1-inch pieces. Place the florets and stems (about 7 cups) in a large bowl. Drizzle with 2 tablespoons of the olive oil, season with ½ teaspoon kosher salt and ¼ teaspoon black pepper, and toss to combine.

Transfer onto the hot baking sheet, spread into a single layer, and arrange the pieces so they are cut-side down. Return the baking sheet to the oven and roast until the broccoli is starting to brown, about 20 minutes. (This is a good time to toast the breadcrumbs and make the dressing.) Toss the broccoli and roast until crisp-tender, about 5 minutes more.

Heat the remaining 2 teaspoons olive oil in a small frying pan over medium heat until shimmering. Add ¼ cup panko breadcrumbs and a pinch of kosher salt. Cook, stirring frequently, until golden-brown and toasted, 2 to 3 minutes. Remove the pan from the heat.

Juice 1 medium lemon into a small bowl until you have 4 teaspoons. Add 1 cold large egg yolk or 1 tablespoon mayonnaise, 1 teaspoon Dijon mustard, ⅛ teaspoon kosher salt, and a few grinds of black pepper, and whisk to combine. While whisking constantly, slowly drizzle in ¼ cup neutral oil until thickened and combined.

Finely grate until you have 2 tablespoons Parmesan cheese. Chop 1 ½ anchovy fillets and 1 garlic clove together until paste-like (if using anchovy paste, add ¾ teaspoon directly to the dressing). Add the cheese, anchovy, and garlic to the dressing and whisk until combined.

When the broccoli is ready, place the baking sheet on a wire rack. Drizzle with all of the dressing and toss to coat. Transfer to a serving plate. Sprinkle with the breadcrumbs. Finely grate a generous amount of Parmesan cheese (about ½ ounce), preferably with a Microplane, over everything.