Trim and discard the top 1/2 inch from the artichokes. Remove and discard any dark outer leaves and peel the stems. Using a large knife, very thinly slice the artichokes lengthwise.
In a large enameled cast-iron braiser or Dutch oven, heat 1 inch of canola oil until shimmering. Line a large baking sheet with paper towels. In batches if necessary, fry the artichoke slices over medium-high heat, stirring occasionally, until browned and crisp, 4 to 5 minutes. Using a slotted spoon, transfer the frizzled artichokes to the prepared baking sheet to drain; sprinkle with salt.
In a medium bowl, toss the frizzled artichokes with the lemon zest and parsley; season to taste with salt and pepper.
Ladle the soup into bowls and top with the frizzled artichokes. Drizzle with olive oil, sprinkle with paprika, and serve, passing more yogurt at the table.