Preheat oven to 365 degrees. Prepare two baking sheets with foil and cooking spray. Bring a small pot with quinoa and 1 cup water to a boil over high heat. Reduce to a simmer, cover and cook for 10-15 minutes, or until tender and all liquid has been absorbed. Thoroughly rinse produce and pat dry. Peel and cut sweet potato into 1/2" dice. Zest lemon and mince zest. Halve lemon and juice. Trim ends off parsnips and peel. Use peeler to cut thin strips from parsnips. Cut those strips into 2" pieces.

Mix parsnip, 2 Tbsp. olive oil, and 1/4 tsp. salt on prepared baking sheet. On second baking sheet, toss sweet potatoes, 1/2 tsp. olive oil, and a pinch of salt and pepper. Place parsnips on top rack of oven, and sweet potatoes on bottom rack, and cook 15-20 minutes, or until sweet potatoes are tender. Remove sweet potatoes from oven and sprinkle with half of the seasoning mix. Flip parsnips over and bake 10-15 minutes more, or until they are golden brown. Watch parsnips closely, as they brown quickly. You may have to pull some of the chips out if they finish first and allow the rest to keep baking. Sprinkle chips with remaining seasoning mix.

While waiting for parsnips and sweet potatoes to cook, stir together mayonnaise, lemon zest, and 2 tsp. lemon juice in a small bowl and set aside in refrigerator.

Add sweet potatoes and half the panko breadcrumbs to quinoa in small pot. Mash with a potato masher or fork. This mixture should stay relatively chunky and not be smooth like mashed potatoes. Check mixture for dryness. If needed, add 1 Tbsp. water at a time, checking each time to see if mixture will easily hold together when compressed. Taste and season with salt and pepper. Divide mixture into 4 balls. Roll balls in remaining panko and flatten each ball using the palm of your hand to form 3" wide patties.

Heat a medium non-stick pan over medium heat. Cut cheese slices on the diagonal. Add 2 Tbsp. olive oil to hot pan and place patties in pan. Reduce heat to medium and cook patties until browned on the first side, about 3 minutes. Flip patties, place half a slice of cheese on each patty, and cook for 3-4 minutes, or until bottom is browned and cheese has begun to melt. Remove burgers from pan and place buns in to toast. Keep heat moderate to ensure patties warm all the way through without burning the panko crust.

Spread lemon mayonnaise on bun. Place burgers on bottom buns and top with arugula and top buns. Place sliders on a plate next to parsnip chips.