Heat 2 tablespoons oil in a large skillet. When hot enough to sizzle a piece of artichoke heart, add the artichokes, cut sides down, and cook over medium heat until golden brown, about 5 minutes. Turn, sprinkle with salt and a generous grinding of black pepper and brown the other sides, about 5 minutes. Transfer browned artichoke hearts to a bowl.
Add remaining 2 tablespoons oil, the shallots and garlic to pan and cook, stirring, over low heat until sizzling. Add carrots, green beans and 1/4 cup water. Sprinkle with 1/2 teaspoon salt and a grinding of black pepper and cook, covered, until vegetables are crisp-tender, about 5 minutes.
Add asaparagus and peas and cook, stirring, uncovered, until asparagus is crisp-tender, about 3 minutes. Add artichokes and dill and cook, stirring, over medium-low heat until artichokes are heated through, about 2 minutes. Serve with lemon wedges to squeeze over each serving.