Prepare the zucchini using a spiralizer and place in a large bowl.
Preheat oil in a large skillet over medium high heat. Add tomatoes and cook, stirring occasionally, until bursting and blistered, 6-7 minutes. Remove from heat and toss with vinegar. Season with salt and pepper and set aside.
To make the Basil Walnut pesto, mix all the ingredients in a food processor until everything is well blended with no clumps.
Add the pesto on top of the zoodles and mix with blistered tomatoes. Season to taste, top with grated Parmesan and basil, and serve as a cold salad immediately.
Storage: This pesto zoodle salad is best enjoyed close to it being made. As the zoodles sit they will start to release water, so it's best to enjoy on the same day. If you have leftovers, store in an airtight container for up to 2 days.