Stir together shallot and vinegar in a small bowl. Stir in ¼ teaspoon fine sea salt and ⅛ teaspoon black pepper; let stand 15 minutes. Meanwhile, place a fine wire-mesh strainer over a medium bowl. Squeeze tomato halves into strainer, pressing on solids to extract about ½ cup tomato juice; set juice aside. Discard tomato halves.
Transfer shallot to a large bowl using a slotted spoon. Add shallot-infused vinegar, mustard, and honey to bowl with tomato juice, and whisk to combine. Gradually add olive oil in a thin, steady stream, whisking constantly until thickened and well combined. Whisk in remaining ¼ teaspoon fine sea salt and remaining ⅛ teaspoon black pepper.
Transfer ⅓ cup vinaigrette to large bowl with shallot. Add greens, and toss to coat. Sprinkle with flaky sea salt; serve immediately with remaining vinaigrette on the side.
