Step 1

Cut tomatoes in half crosswise. Place a box grater in a large bowl. Grate tomatoes, cut side against the coarse side of the grater, until only the skin remains; discard skin. You should have about 2 1/2 cups of grated tomatoes with juices. Set aside.

Step 2

In a large skillet, heat grapeseed and olive oils over medium heat. Add onions and cook, stirring often, until deep golden brown, adding more oil if onions are sticking, about 15 minutes. Mix garlic into onions.

Step 3

Add grated tomato and cook, stirring occasionally at first, then often during the last 15 minutes or so, until all the liquid has evaporated, mixture is reduced by 3/4 and is deeply red and caramelized, and you begin to see a separation of oil from the vegetables, 30 to 40 minutes. Add a splash of water to skillet to loosen any bits from the bottom of the pan and stir until evaporated. Let cool.

Step 4

Set 3 tablespoons sofrito aside for arroz. Divide remaining sofrito into smaller portions in freezer-safe containers or an ice cube tray. Refrigerate or freeze for later use.

Step 5

In a food processor, process egg, garlic, lemon juice, and salt to blend. With the machine running, gradually add oil, processing until smooth. Season to taste with salt. Transfer to a small bowl.

Step 6

In a large skillet, heat grapeseed and olive oils over medium-high. Add protein and cook, stirring or turning occasionally, until browned, 3 to 8 minutes, depending on the protein; transfer to a plate. Add vegetables, season with salt, and cook, stirring often, until browned in spots, 3 to 5 minutes; add to plate.

Step 7

Add sofrito to skillet and cook until heated through, 30 seconds to 1 minute. Add sherry and stir, scraping up browned bits on the bottom of the pan. Add stock. Season generously with salt, bring to a simmer, and stir in rice.

Step 8

Bring stock to a simmer and cook for 5 minutes (do not stir rice). Add protein to skillet, arranging it evenly over rice. Continue cooking (do not stir) until rice starts to come to the surface of the stock, the edges are foamy, and it begins to make a crackling sound, about 5 minutes. Add vegetables and herbs to skillet, spreading evenly over the top of the rice. Reduce heat to low and cook until rice is al dente, edges are darkened, and rice smells very toasty, about 5 minutes more. Remove skillet from heat, cover, and let rest for 5 minutes before serving.