Preheat the oven to 425°F. Prepare a large rimmed baking sheet.
Arrange the cubed celery root, chopped cauliflower, peeled apples, halved leeks, and whole garlic cloves on the baking sheet.
Season with paprika, kosher salt, and freshly ground black pepper. Drizzle with 2 tablespoons of extra virgin olive oil and toss to coat.
Spread the vegetables into an even layer and roast for approximately 25 minutes, flipping halfway through, until tender and lightly golden. If necessary, continue roasting until the celery root is fork-tender.
Transfer the roasted vegetables to a large pot or Dutch oven.
Add the chicken bone broth, fresh thyme sprigs, and sage leaves.
Bring the mixture to a boil, then cover, reduce the heat to low, and simmer for approximately 45 minutes to allow the flavors to develop.
Remove the thyme sprigs and sage leaves.
Using an immersion blender, carefully puree the soup until completely smooth and creamy.
Alternatively, transfer the soup to a countertop blender in batches, following the manufacturer's instructions for blending hot liquids.
Add the crème fraîche or mascarpone cheese and unsalted butter to the blended soup.
Blend again until completely incorporated and silky smooth.
Return the pot to low heat and gently simmer for another 10 minutes, stirring occasionally.
Taste and adjust the salt and pepper as needed. Add a splash of additional broth if the soup is thicker than desired.
While the soup finishes simmering, drain the canned artichokes thoroughly and pat dry with paper towels.
Roughly chop the artichokes and toss with 1½ tablespoons of cornstarch and a pinch of salt until lightly coated.
Heat enough olive oil to coat the bottom of a large skillet over medium heat.
Test the oil with a small artichoke piece. If it sizzles gently, add the remaining artichokes in a single layer.
Cook, turning occasionally, until golden brown and crispy.
Transfer to a paper towel-lined plate to drain. (You may need to do this in batches in order to not overcrowd the pan).
Ladle the warm soup into serving bowls.
Top with rye croutons, crispy artichokes, and freshly chopped chives.
Finish with a drizzle of good extra virgin olive oil and a small sprinkle of licorice salt, if desired.
Serve immediately.