Snap the asparagus by the ends and chop into bite sized pieces. Heat a saute pan with 1 tsp olive oil and add asparagus, let saute for 1 minute. Add broth and cook until broth evaporates and asparagus are cooked, but still a bit crunchy (you don't want mushy asparagus).
Spiralize zucchini and set aside. Slice the tomatoes. In a food processor, add all the pesto ingredients, except the oil. Process while slowly adding oil through the top. Keep pulsing until well combined, scraping down sides, if needed.
Toss zoodles with some of the pesto and place in a serving bowl. Top with asparagus and cherry tomatoes. Serve immediately.