Fill a large bowl with cold water and squeeze in half a lemon.

Trim each artichoke — cut off the top third, snap off dark outer leaves until you reach the pale yellow-green inner leaves, and peel the stem.

Halve each artichoke and scoop out the fuzzy choke. Rub cut surfaces with lemon and drop into the lemon water.

Bring a large pot of salted water to a boil. Add garlic cloves, bay leaf, and artichoke halves.

Simmer until completely tender when pierced with a knife — about 15-20 minutes.

Drain and let cool. Remove bay leaf. Reserve garlic cloves.

Add cooked artichoke hearts, reserved boiled garlic, Kalamata olives, capers, raw garlic, lemon juice, and olive oil to a food processor.

Pulse until chunky — 5-6 pulses. Do not over-process.

Transfer to a bowl. Fold in chopped parsley. Season with salt and pepper.

Whisk egg yolk, grated garlic, lemon juice, lemon zest, and salt together in a bowl.

Add neutral oil drop by drop, whisking constantly, until the emulsion takes hold.

Increase to a slow, steady stream while whisking until all oil is incorporated and aioli is thick and glossy.

Taste and adjust salt and lemon as needed.

Spoon artichoke tapenade onto each cracker.

Drizzle lemon aioli over the top.

Squeeze fresh lemon over the artichoke.

Finish with flaky sea salt.