Preheat the oven to 425F convection 450F regular bake. Line a baking sheet with parchment paper.
Add the potatoes, 2 tablespoons oil, 1 teaspoon salt, and pepper. Toss to coat, then spread out into an even layer, placing the potatoes cut-side-down. Bake for 15 minutes.
Pat the artichokes as dry as you can. Add them to a large bowl and use your hands to gently toss in the remaining 1 tablespoon oil and ½ teaspoon salt. Scatter them onto the baking sheet, nestling them among the potatoes, and bake for 20-25 more minutes or until potatoes are deeply golden on the bottoms and artichokes are browned/charred in spots.
Let the veggies cool down a bit, then add greens (if using) to the baking sheet along with the vinegar and toss to coat and mix it all together (the greens should soften a bit). Serve it warm on the baking sheet or transfer to a large platter. Top with eggs, radishes, cheese, and herbs. Drizzle all over with olive oil and sprinkle with salt and pepper.