Heat the oven to 425 degrees and line 2 baking sheets with parchment paper.
Trim off the bottom of the broccoli stalks. Cut the stalks crosswise just under the florets and separate the florets into large pieces. Slice off or peel the outside of the stalks and cut crosswise into 1" pieces. Toss onto a baking sheet.
Thinly slice off the root ends of the onion and slice in half through the roots. Peel and slice into 1" thick wedges or pieces. Add to the broccoli.
Peel the potatoes and cut into 1/2" cubes. Repeat with the sweet potatoes. If you'd prefer to keep the peel on, scrub under running water and dry thoroughly, then cut into cubes. Add to the broccoli and onion.
Toss all the veggies with the avocado or olive oil, salt, freshly ground black pepper and red pepper flakes (if using). If the onions separate that's okay. Divide evenly onto both sheets and spread out in an even layer.
If the salami slices are large, cut into half moons or quarters. Distribute evenly over the vegetables on both pans. Roast everything for 35-40 minutes, rotating and swapping the pans halfway through.
Meanwhile, mince the fresh rosemary and thyme.
When the veggies are done, take the trays out and use a spatula to first toss the veggies around and then scoot them around, creating wells for the eggs. Crack the eggs into the wells and return to the oven. Bake for another 5 minutes for runny yolks, 8 minutes for medium yolks and 10 minutes for hard yolks.
Remove from the oven. Sprinkle flaky sea salt and freshly ground black pepper over the eggs and the fresh herbs over everything.