Bring a large pot of water to a boil. Add the potatoes and boil for 10 minutes or until tender. Add the carrots to the pot and boil an additional 5 minutes. Vegetables should be tender enough that they can be pierced with a fork.
While the potatoes cook, combine all of the ingredients for the pesto in a food processor. Slowly add the olive oil. Blend until well combined. Add more olive oil for a thinner pesto. Set aside until ready to serve.
Rinse potatoes and carrots under cold water and cube small enough to add to a blender. In a blender combine potatoes, carrots and cream. Mix until just started to resemble mash potatoes. Do this step in batches if needed.
In a large bowl, combine mixture with green onions, 1/2 cup parmesan, flour and cornstarch. Fold together until fully incorporated. Season with salt and pepper. Use a cookie scoop to form balls and place on baking tray. Refrigerate for 30 minutes.
In a non stick pan, heat olive oil over medium heat. Add just enough to the pan to cover the bottom for a shallow fry. While the oil warms, combine the remaining parmesan with bread crumbs in a shallow bowl. Use your hands to flatten the balls into small patties. Coat both sides with the parmesan/panko mixture. Cook until golden about 4 minutes per side. The edges should begin to change colours and crisp once you see this they are ready to be flipped. Remove from heat and set on paper towel lined plate. Repeat until all the patties are cooked.
Serve warmed topped with pistachio pesto.