Prepare the ingredients: Scrub the mussels or clams; place them in a bowl with the shrimp. Slice the zucchini and mushrooms; chop the cauliflower into bite sized pieces. Add the vegetables to a bowl. Mince the garlic, then add it to a small bowl with the olive oil. In a medium bowl, mix together the tomato puree and broth. In a another bowl, add the Arborio rice, saffron, pimentón, kosher salt, and a good amount of fresh ground pepper.
Assemble the paella: Bring the bowls of ingredients and the paella pan to the grill. Prior to cooking, add about 15 briquettes to the fire to keep the temperature up. Place the pan on the grill and add the olive oil and garlic; cook for about 30 seconds. Add the vegetables; cook for about 2 minutes, stirring occasionally. Add the seafood; cook for about 2 minutes, flipping the shrimp once. Pour in the rice and spices so that they cover the pan. Add the broth and puree mixture and stir to combine.
Let the paella cook for 20 to 30 minutes, until most of the liquid has evaporated. Cook uncovered on a charcoal grill or with the cover down on a gas grill. Make sure not to stir, since this when the magic happens (the crust on the bottom is the most important part of a traditional paella). Also be careful that is does not burn; it cooks fairly quickly.
After removing from the heat, let sit for about 5 to 10 minutes to cool.