How to Make It
Let pizza dough rest at room temperature for 30 minutes. (Keep dough covered to prevent drying.)
Place a pizza stone or large, heavy baking sheet in oven. Preheat oven to 500°F. (Do not remove pizza stone while oven preheats.)
Combine 6 cups water and lemon juice in a large bowl. Trim artichoke stems to within 1 inch of base. Peel remaining stem attached to artichoke. Quarter each artichoke lengthwise; place in lemon water.
Trim onions to 6 inches in length; halve each lengthwise. Chop remaining green parts of onions; set aside.
Heat a large cast-iron skillet over high. Add 1 tablespoon oil to pan; swirl to coat. Add the onion halves, cut sides down. Cook until lightly charred, about 2 minutes; turn over, and cook 1 minute. Remove onion halves from skillet.
Drain artichokes; pat dry with paper towels. Add 1 tablespoon oil to skillet; swirl to coat. Add artichoke quarters; cook until lightly charred on all sides, about 6 minutes, turning occasionally. Remove the artichokes from skillet.
Place pizza dough on a lightly floured surface; roll into a 12-inch circle. Combine ricotta, milk, lemon zest, pecorino Romano, chopped green parts of onions, and half of the garlic in a bowl. Spread mixture over dough, leaving a 1-inch border. Arrange charred onions and artichokes, cut sides up, over ricotta mixture. Carefully slide pizza onto hot pizza stone. Bake at 500°F until crust is lightly browned and crisp, 8 to 10 minutes.
Combine remaining 1 tablespoon oil and remaining half of garlic in a small microwavable bowl. Microwave on high until fragrant, about 40 seconds. Brush oil mixture on edges of pizza crust. Sprinkle pizza evenly with salt and crushed red pepper; top with parsley and dill. Cut into 8 slices.