Make the dressing
Whisk the lemon juice, mustard, salt, and pepper in a small bowl. Slowly whisk in the oil until combined. Whisk in the garlic, marjoram, and red pepper flakes.
Make the salad
Combine the vinegar and 2 tsp. salt in a large bowl. Let sit to dissolve the salt. Put the potatoes and 2 Tbs. salt in a 6-quart pot and add enough cold water to cover by 1 inch. Bring to a boil over high heat and reduce the heat to maintain a simmer. Cook the potatoes until barely tender when poked with a fork or skewer, 5 to 10 minutes. If the potatoes aren't all the same size, remove them as they are cooked.
Gently drain the potatoes in a colander and set aside until just cool enough to handle. Cut the potatoes into 3/4-inch chunks. Add the potatoes to the bowl with the rice vinegar and gently stir with a spatula to coat. With your fingers, pull apart any pieces that are stuck together.
In a large skillet, heat the olive oil over medium-high heat. Add the artichoke hearts and a sprinkle of salt, and cook, turning once, until browned on both sides.
Gently fold the browned artichokes, olives, and chopped mint into the potatoes. Whisk the vinaigrette back together and fold enough of it into the potatoes to generously coat them (you may not need all of the dressing). Season to taste with salt and pepper. Serve while still slightly warm, or at room temperature.