Prepare the artichokes: Squeeze the lemon into a bowl and add cold water. As you work, dip the artichokes in this lemon water. It will stop them from turning brown.
Using a sharp knife, slice off the top third of the artichoke. You should see the pale green center leaves and even some purple. Scoop out those center leaves and the choke with a melon baller or teaspoon. Slice off the stem and peel away any little leaves near the base. Use kitchen scissors to cut off tips of outer petals. Transfer to the water.
Make the stuffing: Mix the almond meal, parmesan, parsley, anchovies, capers, garlic, and red pepper flakes. Taste and adjust seasoning with salt and pepper.
Preheat your oven to 400. Remove the artichokes from water and pat dry. Stuff artichokes with filling and transfer to a large lidded skillet or Dutch oven. Add the wine and add enough water so that the liquid comes 1 inch up the sides. Cover the pan and bring to a boil. Reduce to a simmer and cook until artichokes are tender, about 30 minutes.
Uncover the pan and transfer to your oven. Roast until the stuffing is toasted, about 10 minutes. Remove artichokes from saucepan and serve with lemon garlic on the side.