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 Tbs. 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 tsp. of the basil purée 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.