In a 14-inch paella pan (or any wide, shallow skillet), add the oil and warm over medium-high heat. Once the oil is hot, add the garlic, green beans, butter beans and artichokes and sauté for about 3-4 minutes.
Add the tomatoes, smoked paprika, saffron and salt. Mix everything together well, then pour in the broth.
Bring the mixture to a boil, then sprinkle the rice in, trying to distribute it evenly throughout the pan.
Bring the mixture to a boil again, then reduce heat to medium-low. You want to see the rice is cooking, but not boiling hard, so adjust heat as necessary. Don't stir after this point!
Simmer for 15-20 minutes, uncovered, until the rice is tender and the broth is cooked off. Carefully rotate the pan every 5 minutes or so. If for some reason the rice is still crunchy after the broth has cooked off, add 1/4 cup more broth and continue cooking. This means your heat was a bit too high.
Once the broth is about cooked off, listen for any crackles or pops from the bottom of the pan. You should also smell a nutty aroma from the crust forming. As soon as you hear any pops, remove from heat. If it smells like it's burning at all, remove from heat immediately. You are hoping for a golden, crisp rice crust.
Garnish with lemon slices and chopped parsley, if desired and serve.