Start the batter: Set a large nonstick skillet and a paper towel-lined plate near the stove. Drain the artichoke hearts and cannellini beans in a colander.

Spread the artichoke hearts on a clean kitchen towel or more paper towels and press firmly to remove as much water as you can. Finely chop the artichokes and put them into a medium bowl.

Thinly slice the shallot. Add half of the shallot to the bowl with the artichokes and set the other half aside for the beans.

Zest the lemon into the bowl. Cut the lemon in half and squeeze the juice into a small cup so it is ready later.

Crack the eggs into the bowl and beat them with a fork until no streaks remain.

Add the flour, 1/3 cup of the Parmesan, 1/2 teaspoon of the salt, and 1/4 teaspoon of the black pepper to the bowl. Stir until you have a thick batter that can be scooped with a spoon.

Let the batter sit for 5 minutes. This short rest gives the flour time to absorb moisture so the fritters hold together better in the skillet.

Warm the beans: Put a medium saucepan on the stove over medium heat. Add 1 tablespoon of the olive oil and the reserved shallot.

Cook the shallot in the saucepan for 2 to 3 minutes, stirring often, until it softens and smells sweet but is not browned much.

Add the drained cannellini beans and 1/4 cup water to the saucepan. Stir gently and cook for 3 to 4 minutes, until the beans are hot all the way through.

Add the arugula, 1 tablespoon of the lemon juice, 1/4 teaspoon of the salt, and a few grinds of black pepper to the saucepan. Stir until the arugula wilts into the beans, about 1 minute, then turn the heat to low to keep the beans warm.

Fry the fritters: Put the large skillet over medium heat. Add 2 tablespoons of the olive oil and heat it until it looks shiny and moves easily around the pan.