In a medium bowl, whisk together the parmesan, vinegar, mustard, anchovies, garlic, and egg yolks.
Zest in the lemon and squeeze in the juice, then whisk in 5 tablespoons of olive oil until emulsified.
Season with salt and pepper and set aside.
Heat the oven to broil.
Cut the broccoli florets into 3-inch long spears. Trim off the stems and peel.
Halve the stems lengthwise, then cut into ¼-inch thick slices.
Toss the broccoli florets and stems with the remaining 3 tablespoons of olive oil, the salt, and pepper and spread into an even layer.
Broil, tossing the broccoli once halfway through, until blackened, about 15 minutes.
Meanwhile, toss the bread with the chili oil, chilis (if using), salt, and pepper.
Broil until golden, about 2 to 3 minutes.
In a large bowl, toss the broccoli, chilies, and croutons with the dressing.
Transfer to a serving platter and grate fresh parmesan over the top.
