Step 1Massage the saffron with your thumb and fingers and place in a ramekin or small bowl. Cover with 2 tablespoons hot water.
Step 2Heat 2 tablespoons of the oil in a wide skillet or paella pan over medium heat. Add the onion and cook, stirring often, until tender, 3 to 5 minutes. Add the turnips and cook, stirring, until they just begin to color and become tender, 10 to 12 minutes. Add the garlic and continue to cook, stirring often, until the garlic is fragrant, about 1 minute. Season with 1/4-teaspoon salt and several grinds of pepper, or to taste. Remove to a bowl.
Step 3Add the remaining oil to the pan, and when hot, add the rice. Stir over medium heat until the rice begins to crackle and is thoroughly coated with oil. Continue to cook until the rice feels heavy and begins to stick to the pan, 3 to 4 minutes. Stir the turnip and onion mixture into the rice, add the saffron, the broth (rinse out the ramekin with a little broth), and salt to taste (this will depend on the saltiness of your broth; the rice should be well seasoned). Add the peas and white beans, bring to a boil and stir once. Reduce the heat to low and simmer until the broth has been absorbed, 20 to 25 minutes.
Step 4Leave the rice over the heat until a layer begins to stick to the bottom, about 5 minutes. Remove from heat and cover tightly. Set the paella aside to rest for 10 minutes. Check the rice at the edges of the pan and, if not quite chewy enough, stir toward the middle, cover again and set aside for another 10 minutes. Drizzle a little olive oil over the top if desired and serve, passing aioli at the table for guests to spoon on.