Trim the stems off of the artichokes and rinse them under cold water. Cut the top ½ inch or so off of the top of each artichoke and trim the sharp tips of the leaves off with kitchen scissors.
Fill a pot with a few inches of water and set a steamer basket over it. Bring the water to a boil and place the artichokes in the steamer basket. Cover with a lid and steam for 35 minutes. Remove the artichokes from the steamer basket and let them drain on a paper towel.
Once cool enough to handle, spread the petals of an artichoke gently and pull out the tender center petals to expose the fuzzy center of the artichoke. Use a spoon to scoop out the fuzzy center. Repeat with the second artichoke.
Preheat the oven to 400°F and grease an 8X8-inch baking dish.
Heat a large saucepan over medium heat and add 2 tablespoons of butter. Once the butter has melted, add the shallot and cook until translucent. Add the garlic and cook until fragrant.
Deglaze the pan with white wine and lemon juice. Cook for 4 minutes.
Melt the remaining butter in the pan.
Turn off the heat and stir in the parsley and breadcrumbs. Stir until the breadcrumbs are completely coated in the buttery sauce. Season with salt and pepper to taste.
Arrange the artichokes stem-side-down in the baking dish. Spoon the stuffing into the middle of the artichokes and between the petals. Sprinkle the tops with parmesan cheese and drizzle with olive oil.