Prepare a large bowl of ice water. Cook the beans in a large pot of boiling salted water for 3-4 minutes, until crisp-tender. Drain, then submerge in the ice water bath to fully cool. Drain again, and pat dry with a kitchen towel. Transfer to a large bowl.
In the bowl of a food processor, combine the almonds, cheese, garlic, thyme leaves, crushed red pepper, and salt. Process to form a coarse paste. Add the vinegar and pulse to combine. Pour in the olive oil, and stir to combine. Add more salt or pepper flakes to taste.
Top the green beans with almond pesto and toss to coat. Drizzle with a bit of olive oil, top with the tomatoes, and serve.