8 to 10 small waxy potatoes (about 1 ounce each), scrubbed and quartered
1 cup vegetable or another broth; just use salted water if you don’t have it around
1/4 cup olive oil
8 ounces (usually 1 bundle) broccolini, trimmed and halved lengthwise or chopped into 1-inch pieces
1 small red or white onion, thinly sliced
8 large eggs
1 cup (about 3 to 3 1/2 ouncesgrated Parmesan cheese
Salt and freshly ground black pepper, to taste