Spritz 4 to 5 pieces of newspaper with vegetable oil and put in the bottom of a charcoal chimney starter. Fill the chimney with half of the charcoal and light the newspaper.
When the charcoal is lightly covered with gray ash, carefully pour onto the bottom grate of a kettle grill and spread evenly. Top with the remaining unlit charcoal, spreading evenly so as not to suffocate the lit charcoal. Set the second grate in the kettle and cover until ready to cook.
Meanwhile, halve the tomatoes and remove the seeds to a fine-mesh strainer set over a small bowl to catch the juice. Grate the seeded halves on the large hole side of a box grater and discard the skins. Combine the reserved juice and grated tomato and set aside.
Warm the chicken broth in a kettle or 4-quart saucepan over high heat until it reaches 200ºF. Remove the broth from the heat and cover to keep warm.
Combine the rice, saffron, rosemary, 1 teaspoon of the salt, and paprika in a small mixing bowl.
Heat the olive oil in the paella pan on the prepared grill. Season the chicken on all sides with the remaining 2 teaspoons of salt. Once the olive oil shimmers, add the chicken and cook until golden brown on both sides, 5 to 6 minutes per side. Move the chicken to the outer edges of the pan. Add the green beans, red bell pepper, green bell pepper, and garlic to the center of the pan and cook until they begin to soften and darken in color, 2 to 3 minutes. Add the tomatoes and their juice and cook until most of the liquid has dissipated and the tomatoes thicken and darken, 4 to 5 minutes.
Add the rice mixture to the center of the pan and cook, stirring constantly for 1 minute.
Redistribute the chicken pieces on top of the rice. Add 4 cups of the warm chicken broth and stir to distribute the rice evenly in the pan, making sure that all rice is completely submerged in liquid. From this point forward, do not stir the paella. When all of the liquid is absorbed and the rice appears dry, 8 to 9 minutes, add an additional 4 cups of broth. Continue to cook, without stirring, until the liquid is absorbed, another 8 to 9 minutes. The rice should be firm to the bite and the grains have a tiny white dot in the center. Add the remaining cup of broth, as needed, until the rice is cooked through. Watch the fire to make sure it is heating evenly and adjust the pan to prevent uneven cooking.
Remove the pan from the heat, cover with a tea towel, and rest for 15 minutes before serving.