In a small bowl, whisk together shallot, vinegar, and salt. Add ½ cup olive oil in a slow stream, whisking until emulsified, and set aside.

Cut tomatoes crosswise into ½-inch-thick slices and arrange on a platter or on four small plates. Cut halloumi into ¼-inch-thick slices. Heat remaining 2 teaspoons olive oil in a medium-size nonstick frying pan over medium-high heat, and fry halloumi slices until golden brown, about 2 minutes per side. Arrange cheese over tomatoes, and drizzle shallot vinaigrette on top. Tear basil leaves over top. Sprinkle with pepper, if you like. Serve immediately.