FOR THE CELERY ROOT: Working in 2 batches, pulse celery root in food processor until finely chopped, about 20 pulses per batch; transfer to bowl. Pulse potato in processor until finely chopped, about 10 pulses, and add to bowl with celery root. (You should have about 9 cups chopped vegetables.)

Melt butter in large saucepan over medium heat. Stir in celery root–potato mixture, water, salt, and baking soda. Cover and cook, stirring often (mixture will stick but cleans up easily), until vegetables are very soft and translucent and mixture resembles applesauce, about 30 minutes. While celery root cooks, make topping.

FOR THE TOPPING: Melt butter in 8-inch nonstick skillet over medium-high heat. Add sage and shallot and cook, stirring frequently, until sage is crisp and shallot is golden, about 3 minutes. Off heat, stir in pepper and salt. Cover to keep warm.

Uncover celery root mixture and cook, stirring vigorously to further break down vegetables and thicken remaining cooking liquid, about 1 minute. Transfer celery root mixture to clean, dry food processor. Add cream and process until smooth, about 40 seconds. Season with salt to taste. Transfer to serving bowl, drizzle with topping, and serve. (Ungarnished puree can be cooled and refrigerated for up to 2 days. Before serving, microwave puree on medium-high power in covered bowl, stirring often, until hot throughout, 7 to 10 minutes.)