• Preheat the oven to 400°F and line a baking sheet with parchment paper.

Prepare the Artichokes:

• Cut just the top tips of the artichokes crosswise, trim the sharp points of the leaves with scissors, trim the stem, and peel the stem while also removing small leaves around the bottom.
• Cut the artichokes in half lengthwise and immediately squeeze and rub lemon juice from one lemon all over them.
• Scoop out the fuzzy part of artichokes with a spoon and discard.
• Squeeze the other lemon into the wells of the artichokes.
• Put the artichokes and halved garlic heads cut side up on the parchment lined baking sheet.
• Sprinkle everything with salt and pepper and drizzle with olive oil.
• Add the finely chopped shallots to the wells of the artichokes.
• Flip both the artichokes and garlic heads over so the cut side is down.
• Oil, salt and pepper the backs of the artichokes.

Roast the Artichokes:

• Cover the entire baking sheet with aluminum foil and roast for 45 minutes or until the artichokes are tender.
• Remove the foil and pop them back in the oven for another 10 to 15 minutes until the bottoms of the garlic and artichokes have browned.
• Remove from the oven and transfer the artichokes to a serving platter, scooping any shallots stuck to the bottom onto the tops of the artichokes. Reserve the garlic heads for the sauce.

Make the Creamy Garlic Sauce:

• Squeeze the roasted garlic into a bowl, mash with a fork until a paste forms.
• Combine the garlic with the sour cream, mayonnaise, mint, parsley, dill, lemon zest and juice, and add salt and pepper to taste.

Assemble the Dish:

• Add capers, roughly chopped mint, parsley, dill sprigs, and lemon wedges to the plate and serve the sauce on the side for dipping.