Combine 2 cups vegetable stock and quinoa in a saucepan. Bring to the boil. Reduce heat to low and simmer, covered, until quinoa is tender, about 20 minutes.
Meanwhile, heat 1 tablespoon olive oil in a large deep frying pan over medium-high heat. Add mushrooms and cook, stirring occasionally, until browned, about 4 minutes. Add 1 tablespoon white wine and let it cook down with the mushrooms, about 3 minutes. Transfer mushrooms to a bowl.
Reduce heat to medium and heat 1 tablespoon olive oil in the pan. Add onions and paprika. Cook, stirring occasionally, until the onion has softened and browned, about 6 minutes. Sprinkle with flour and cook, stirring, for 2 minutes. Add kale and garlic; season with salt and pepper. Cook until kale is just wilted, about 1 minute.
Stir mushrooms and their juices back into the pan. Add remaining white wine and cook until wine is almost evaporated, about 3 minutes. Reduce heat to low; add remaining vegetable stock. Season with salt and pepper. Cook until sauce is slightly thickened, scraping up any bits that have accumulated at the bottom of the pan, 5 to 7 minutes. Stir in butter until completely melted.
Remove pan from heat and stir in sour cream; season with salt and pepper. Divide quinoa between 2 bowls and spoon kale-mushroom sauce on top. Garnish with parsley.