Preheat oven to 375 degrees. Bring a small pot with quinoa and 1 cup water to a boil over high heat. Reduce heat to medium, then simmer 10 minutes until all water has been absorbed. Reserve. Thoroughly rinse produce and pat dry. Peel and cut sweet potato to 1/2" dice. Zest lemon and mince zest. Halve and juice lemon. Trim ends from parsnips and cut to 1/2" dice. Stem and coarsely chop parsley.

Prepare a baking sheet with foil and cooking spray. On half of the sheet, add diced parsnips, 2 tsp. olive oil, and 1/4 tsp. salt. On the second half of baking sheet, add sweet potatoes, 1 tsp. olive oil, and a pinch of salt and pepper. Toss each half separately to evenly coat and spread into a single layer. Place in oven and bake 15-18 minutes until sweet potatoes and parsnips are tender. Remove from oven and cool for 5 minutes. Sprinkle seasoning mix on sweet potatoes and parsnips. Measure out 2 cups of sweet potatoes to use for burgers. Toss the remaining parsnips and sweet potatoes together and set aside.

While sweet potatoes and parsnips cook, stir together mayonnaise, lemon zest, and 1 Tbsp. lemon juice in a small mixing bowl and refrigerate.

Add to the pot with quinoa, parsley (reserving a pinch for vegetables), panko, and reserved 2 cups of sweet potatoes. Mash using potato masher or fork: mixture should easily stick together when gently pressed but not be sticky. If mixture is too dry, add 1-2 Tbsp. water. (Mix may need nothing or up to 3 Tbsp. water— incorporate 1 Tbsp. at a time.) Season with salt and pepper to taste. Divide mixture into two and roll each half into a ball. Flatten balls into 1" thick patties using the palm of your hand.

Heat a large pan over medium heat. Add 1/2 tsp. olive oil to hot pan and add then patties. Cook until browned on the first side, about 4-5 minutes, then flip. Cook 2-3 minutes, then place cheese slices on top. Cook another 2-3 minutes, until bottoms are browned and cheese has begun to melt. Remove burgers from the pan and toast buns in the same pan. Place parsnip and sweet potato mixture into the oven for 3-5 minutes to reheat.

Spread lemon mayonnaise in bun. Place burger on bottom bun and arugula on top of burger then top with bun. Garnish sweet potatoes and parsnips with remaining parsley and serve next to burger.