This is a springtime country dish from the island of Milos in the Cyclades islands.
Preheat the oven to 350 degrees. Arrange an oven rack so that it's about 8 inches from the heat source of the broiler (which you will use later).
In a bowl, toss the artichoke hearts and potatoes with the oil, garlic, lemon juice, and a little sea salt and pepper. Spread out the mixture evenly in a baking pan large enough to hold the vegetables in 1 layer.
Bake for about 1 hour, just until the artichoke hearts and potatoes are tender. Turn off the oven and turn on the broiler. Broil the vegetables so that the artichokes and potatoes become crusty and brown. Remove from the oven and serve immediately.