Preheat oven to 375°F (190°C).

Prepare the Chimichurri Dip: Combine parsley, cilantro, minced garlic, lemon zest, sea salt, and dried chili flakes in a medium bowl.

In a blender, puree sour cream, mayonnaise, and chopped avocado.

Add a small amount of water if needed to achieve a smooth consistency.

Combine the avocado puree with the parsley-cilantro mixture. Store the chimichurri dip in an airtight container until ready to serve.

Prepare the vegetable chips: Attach the Vegetable Sheet Cutter Attachment to a KitchenAid® Stand Mixer.

Insert the food holder into the center of one end of a sweet potato section and secure it onto the attachment.

Insert a food skewer through the sweet potato, up to the first mark.

Attach the Thin Blade to the attachment.

Position a bowl under the blade to catch the sweet potato sheets.

Turn the Stand Mixer to Speed 2 and position the blade against the sweet potato to process into thin sheets.

Repeat the process with the remaining sweet potato, parsnip, and beet sections.

Transfer the vegetable sheets to a cutting board.

Cut the vegetable sheets into irregular square and triangular pieces, about 2 inches in size.

Toss the vegetable pieces with olive oil and spread them out evenly on 2-3 baking sheets.

Sprinkle the vegetable pieces with sea salt.

Bake the vegetable chips until crisp, 15-20 minutes, turning once halfway through the cooking time.

Remove the baking sheets from the oven and sprinkle the chips with grated Parmesan cheese.

Let the root vegetable chips cool completely before serving with the prepared Chimichurri Dip.