Preheat oven to 350 F, option to line a baking sheet with parchment paper for easy clean up.
Spread asparagus on baking sheet and drizzle with 1 tablespoon of olive oil, 1/2 teaspoon of kosher salt, and 1/4 teaspoon black pepper. Cook until asparagus is just fork tender, about 10-12 minutes.
Meanwhile, combine the parsley, shallot, lemon juice, remaining 1/4 teaspoon salt, and remaining 1/4 teaspoon black pepper. While whisking, slowly drizzle in the remaining 1/3 cup of olive oil.
Assemble the salad by placing asparagus, almonds, parmesan, and tomatoes, together in a large bowl. Drizzle with dressing and toss to combine.