Preheat the oven to 424 degrees F. Alternatively, heat the grill to medium-high.
Remove the plastic film from the potato packaging and set the seasoning packet aside.
Add 2 tablespoons of olive oil and half of the seasoning package to the potato tray. Stir to coat the potatoes. Discard the seasoning packet or save it for another use.
Place the uncovered tray in the oven or on the grill. Cook until the potatoes are tender when pierced with a fork, 30 to 40 minutes.
While the potatoes are cooking, prepare the zucchini noodles. Cut each zucchini in half crosswise. Run the zucchini through the spiralizer to produce noodles.
Place the noodles in a colander set over a bowl and sprinkle them with about ½ teaspoon kosher salt, tossing to coat. Let them rest for 20 to 30 minutes to allow some of the moisture to leach out, then squeeze the zucchini noodles in a clean kitchen towel to release additional moisture.
Heat 2 teaspoons olive oil in a large nonstick skillet set over medium-high heat. Add the green beans and arrange in a single layer on the bottom of the skillet. Cook, stirring once, until the green beans are just tender and browned in some places, about 3 minutes.
Push the greens beans to one side of the skillet and add the remaining 1 teaspoon olive oil to the empty portion of the skillet. Add the garlic and sauté for 30 seconds.
Add the zucchini noodles. Cook, tossing with tongs, until the noodles are just tender. Take care not to overcook, otherwise the smaller zucchini noodles will begin to fall part.
Stir in the potatoes, pesto, salt (taste first before adding), pepper and red chili flakes (if desired). Toss to coat.
Serve immediately with grated Parmesan cheese, if desired.