Combine the scallions, lemon zest & juice, vinegar, and salt and pepper to taste in a small bowl. Stir and let sit for 15 minutes.
Toast the sliced almonds in a medium frying pan over medium-low heat for about 5 minutes, stirring often, until golden brown. Remove from stove top and cool.
Use a vegetable peeler to thinly slice the asparagus lengthwise into strips. When you get down to the last bit, place the spear flat side down on the handle of a spatula to allow the peeler to move freely. Pace sliced spears in a large bowl with the quartered tomatoes.
Drizzle the oil into the lemon-vinegar mixture in a thin and steady stream, whisking constantly. Season to taste with salt and pepper.
Toss the almonds, mint, half of the cheese, and dressing in with the asparagus and tomatoes. Season again with salt and pepper if desired. Allow salad to sit at least 10 minutes before serving, then top with remaining cheese.