Make the dressing. Mince the anchovies and cloves together. Holding the knife at an angle mash the anchovies and garlic together until a paste forms. Add 1 teaspoon salt and mix until combined. In a separate bowl, whisk yolks until smooth. To eggs, add mustard, anchovy-garlic paste, lemon juice and zest. Pouring slowly, add oil while whisking constantly so that the mixture emulsifies. Continue to whisk while the dressing thickens. Whisk in grated Parmesan and season with black pepper, plus more salt if needed.
Make the toasted breadcrumbs. In a large non-stick or cast iron skillet over medium heat, melt butter. Add breadcrumbs and toss in melted butter. Cook until fragrant and golden brown, tossing in pan occasionally, about 5 minutes (if your pan is too hot, they’ll burn, so keep a close eye). Add lemon juice and zest, salt, and black pepper to taste. Transfer to a bowl and let cool (you might have extra, save in an air tight container for future salad glory).
Assemble the salad. Toss lettuce in dressing. Spread on a platter and top with breadcrumbs, more Parm, a squeeze of lemon, and freshly grated black pepper. Serve immediately.