Heat the oil in a large skillet over medium-high heat.
Add the onion and sauté until translucent, about 3-5 minutes, then add the garlic and sauté for 3 minutes more.
Add the grated carrot, parsnip, and beet, salt, pepper, and dil, and sauté for about 10 minutes, until vegetables have softened.
Remove from the heat and set aside to cool.
Add the beans to the bowl of a food processor and pulse until they've broken down into a paste. Add the quinoa and pulse to combine, then add the cooled vegetables and pulse to combine everything. The mixture shouldn't be completely smooth.
Transfer to a large bowl and mix in the sunflower seeds, sliced green onion, liquid aminos, and nutritional yeast. Mix well.
Preheat your oven to 350°F / 180°C. Line a baking sheet with parchment paper and brush with olive oil.
With clean wet hands, form the mixture into 10-12 burger patties, placing them on the prepared sheet as you go. Smaller patties will hold together better than larger ones, so keep that in mind as you're forming them.
Brush the tops of the patties with olive oil, then place the tray in the oven and bake for 20 minutes.
Remove from the oven and using a spatula carefully turn the patties over. Bake for another 15-20 minutes until they're golden brown on both sides.
Remove from the oven and serve with your favourite burger fixings. Alternately, cool the patties on the tray then place in a freezer bag separated by squares of parchment paper.