Preheat the oven to 350ºF. Line a baking sheet with foil and set a cooling rack on top. Lay the slices of bacon on the rack and roast until golden and crisp, 15 to 20 minutes, turning over halfway through. Transfer the bacon to a paper towel-lined plate. Transfer the bacon grease to a bowl
In a medium bowl, combine the vinegar and shallot; season lightly with salt and pepper.Let stand for 5 minutes, then whisk in the olive oil. Slice the tomatoes into ¼-inch rounds, then into half-moons; reserve.
Spread the mayo on the toasted bread; lay the tomato slices over. Sprinkle the tomatoes with flaky sea salt. Add the mixed greens and basil to the bowl with the vinaigrette bowl; toss to coat.
Transfer the toast to serving plates. Drizzle the tomatoes lightly with reserved bacon grease. Divide the greens among the sandwiches. Top each with bacon and serve.