How to Make It
Bring a large pot of water to a boil over high. Prepare an ice bath in a large bowl.
Using a paring knife, core beefsteak tomatoes. Score an “X” on bottom of each tomato. Carefully drop into boiling water, and cook until skins begin to pull away, about 2 minutes. Remove tomatoes with a slotted spoon, and immediately drop into ice bath to stop the cooking process.
Drain tomatoes, and peel off skins. Reserve tomato skins for Tomato-Skin Salt.
Quarter peeled tomatoes; scoop out seeds and liquid, reserving 1 cup seeds and liquid for Tomato Water Gazpacho (recipe follows). Discard remaining seeds and liquid. Set tomato quarters aside.
Heat oil in a wide, heavy- bottomed pot over medium until shimmering. Add onion, garlic, red pepper, and 1/2 teaspoon sea salt. Reduce heat to medium-low, and cook, stirring often, until onion is translucent, about 8 minutes. (Do not let onion and garlic brown.)
Add tomato quarters and remaining 1/2 teaspoon sea salt. Reduce heat to low, and cook until all moisture has cooked away and tomatoes begin to fry, about 20 minutes.
Remove from heat, and let cool slightly, about 10 minutes. Transfer to a food processor, and process until smooth. Season to taste with sea salt, and transfer to an airtight container. Mixture may be stored in refrigerator up to 5 days.
Stir together vinegar, 1 cup water, kosher salt, and sugar in a medium saucepan until combined. Cook over medium until salt and sugar dissolve. (Do not bring to a boil.)
Place green tomato slices in a sealable container. Pour warm brine over tomatoes, and let cool, uncovered. Pickled tomatoes may be used after 30 minutes or covered and stored in refrigerator up to 5 days.
Preheat oven to lowest possible temperature. Arrange reserved tomato skins from tomato sofrito on paper towels, and blot dry. Spread tomato skins in an even layer on a parchment paper–lined baking sheet. Bake in preheated oven until dry and brittle, 8 hours or overnight.
Transfer dried skins and sea salt to a food processor, and pulse until combined. Store in an airtight container at room temperature.
Cut rind from watermelon; discard rind. Cut watermelon into 15 (3- x 1 1/2- x 3/4-inch) planks; reserve 2 cups scraps for Tomato Water Gazpacho. Set planks aside.
Combine 1 cup tomato sofrito and goat cheese in a food processor. Pulse until smooth; season to taste with sea salt. Transfer mixture to a ziplock plastic freezer bag; snip 1 corner of bag to make a small hole.
Pipe about 2 teaspoons sofrito-cheese mixture over each watermelon plank, spreading evenly into a thick layer. Top each with 2 pickled green tomato slices, and season with tomato-skin salt. Reserve 1/2 cup liquid from pickled green tomatoes for Tomato Water Gazpacho. Sprinkle watermelon planks evenly with sliced herbs.