Spray a disposable aluminum-foil mini loaf pan (5-3/4 x 3-1/4 x 2 inches) with nonstick spray (or lightly grease it) and line it snugly with plastic wrap, leaving about 4 inches hanging over each long side. Put the goat cheese in a small, heatproof bowl and warm it just enough (in a warm oven for 3 to 5 minutes or on the back of a gas range that stays warm from a pilot light) so that it reaches a soft, spreadable consistency; use a small rubber spatula to stir and smooth it out as it's warming.

Arrange a layer of the tomatoes (wrinkled side down) along the bottom of the loaf pan, laying them lengthwise, slightly overlapping; 6 to 8 will fit across the bottom. Drop 2-1/2 tablespoons of the goat cheese in dollops over tomatoes. To spread the goat cheese out into a nice thin layer, use a mini spatula or one or two fingers covered with plastic wrap. Spread 2 teaspoons of the basil puree over the goat cheese in the same way. Repeat three more sets of these three layers -- tomato, cheese, basil -- and finish with a layer of tomatoes. Cover the top of the terrine with the excess plastic wrap and press down gently. Cover and refrigerate for at least 6 hours and up to 24 hours.

To slice and serve the terrine, unwrap the top layer of plastic, cover the terrine with a cutting board, and flip both over to gently force the terrine out. Remove the plastic. Use an electric knife or a very sharp knife run under hot water to slice pieces about 1/2 inch thick. Or use a piece of dental floss to slice: slide a 12-inch piece of floss under the terrine, bring the two ends of floss over the terrine, cross them, leading each back to the direction it came from, and pull each end sharply and quickly to "garrote" a slice. Serve the slices with a small mound of greens and a light drizzle of the vinaigrette.

Heat the oven to 300 degrees F. Fill a large bowl with ice and water. Core the tomatoes and use a sharp knife to score the bottoms with an X. Blanch a few tomatoes at a time for 20 to 30 seconds in boiling water. Remove and shock in ice water for 2 minutes. Start peeling the tomatoes, returning each to the cold water until all are peeled. Quarter the tomatoes and remove the seeds and interior flesh so that just the thick outer flesh is left. (Use a paring knife to carve out insides.) Lay the tomato pieces (seeded side down) flat on a parchment-lined 13x18-inch rimmed baking sheet or jelly roll pan; press down to flatten slightly. Sprinkle lightly with coarse salt and cover with the olive oil. Be sure all the tomato pieces are well coated in oil. Don't worry if they're crowded together; they'll shrink when cooking.

Roast the tomatoes until they're shrunken to one-third their original thickness, 2-1/2 to 3 hours. (You may need to remove the tomatoes in stages, as some will be done before others.) Occasionally turn the pan around in the oven to cook the tomatoes evenly. If the edges are turning black, reduce the oven temperature to 275 degrees F. When done, they'll be wrinkled, flat, and thin, but they'll retain some of their moisture inside. The color will have darkened to a brick red.

Let the tomatoes cool and then store them in the refrigerator (covered in olive oil) for up to two weeks.

Fill a medium bowl with ice water. Bring a large pot of salted water to a boil and blanch the basil for 20 seconds. Dunk the basil in the ice water for a few seconds. Drain well and gently squeeze out excess moisture with towels. Put the basil in a food processor (a mini one works well) with 2 tablespoons of the olive oil. Puree well, adding more olive oil if needed to chop finely. To drain the excess oil, put the puree in a coffee cup or a custard cup lined with a paper coffee filter or cheesecloth for 15 to 20 minutes.

In a shallow bowl, combine the olive puree, anchovies, capers, garlic, shallots, and 3 tablespoons of the vinegar. Whisk in the oil until well combined. Add more vinegar to taste.