Bring a large pot of salted water to a boil. Add the artichokes and cook over medium-low heat for 20 minutes. Remove from the heat and drain. When the artichokes are cool enough to handle, slice them in half.
Preheat the oven to 350°F.
Add the lemon juice, olive oil and garlic to a small bowl and whisk to combine.
Place the artichokes in a small baking dish. Drizzle the lemon mixture over the artichokes and sprinkle the sun-dried tomatoes and Parmigiano-Reggiano over the top. Season with sea salt. Place in the oven and cook for 30 minutes. Remove from the oven.
Transfer to the artichokes to a serving platter and serve immediately.