How to Make It
Combine vinegar, 1 cup water, dill sprigs, sugar, and crushed red pepper in a small saucepan. Bring mixture to a boil over high, stirring occasionally, until sugar dissolves.
Place green tomato slices in a 1-quart wide-mouth glass jar. Pour hot vinegar mixture over tomato slices. Cover with lid; chill 1 to 3 days.
Preheat oven to 200°F. Place grape tomatoes on a parchment paper–lined rimmed baking sheet. Drizzle with 1 tablespoon olive oil, and toss to coat. Arrange tomato halves cut sides up. Sprinkle with black pepper. Bake at 200°F until very soft and dehydrated, about 5 hours. Cool tomatoes to room temperature, about 10 minutes.
Heat canola oil in a large saucepan over medium-high. When oil is very hot but not yet smoking, add cooked farro. Cook, stirring often, until very crispy, about 3 minutes. Using a slotted spoon, transfer farro to a paper towel–lined plate to drain. Let stand 30 seconds; sprinkle with paprika.
Drain green tomatoes; discard liquid. Arrange green tomatoes and heirloom tomatoes on a serving platter. Top with roasted grape tomatoes. Whisk together apple cider vinegar, remaining 2 tablespoons olive oil, and honey in a small bowl. Drizzle tomatoes with dressing, and sprinkle with salt, shallots, torn dill, and fried farro.