Preheat oven to 350F. Line sheet pan with parchment paper.
In a food processor, add the artichokes to the bowl and pulse until finely chopped, not pureed. Pour into a large mixing bowl.
Add the garlic, olives, capers and 1/3 C parsley to the food processor bowl. Pulse until finely chopped, about the same size as the artichokes. Pour into the large mixing bowl with the artichokes.
In a small bowl, whip the lemon juice and olive oil into an emulsion. Pour over the artichoke mixture. Add the sea salt, adjust to taste. If using pepper flakes, add them now. Mix well.
Cut the baguette into 1/2" pieces on the bias. Brush each piece with olive oil. Bake crostini until toasty and golden, about 8-10 minutes, turning the toasts over 1/2 way through baking. Spread artichoke mixture on top of each piece and garnish with optional parmesan cheese, the remaining parsley and a light pinch of sea salt.
Store in a lidded container for up to two weeks in the refrigerator.
Adjust the garlic to your taste. Four large cloves is very spicy and garlicky, two is more moderate.