Preparation Place celery root and potatoes in a large heavy pot. Add cold water to cover; season with salt. Bring to a boil over medium-high heat. Reduce heat; simmer until vegetables can be pierced with a fork, 20-25 minutes. Drain vegetables well. Pass vegetables through food mill or potato ricer into same pot. Meanwhile, bring cream and milk just to a simmer in a medium saucepan; remove from heat. Stir vegetable purée constantly over medium-low heat until excess moisture evaporates, about 2 minutes. Stir butter into purée a few pieces at a time, blending between additions. Remove from heat; slowly fold in cream mixture until a smooth purée forms. Season to taste with salt and pepper. DO AHEAD: Purée can be made 1 day ahead. Cover; chill. Rewarm in a microwave or in a heatproof bowl set over a large pot of simmering water. Strain hot purée through a medium-mesh sieve into a serving bowl (this makes the texture especially smooth and creamy). Drizzle with oil; scatter hazelnuts over.
Preparation Place celery root and potatoes in a large heavy pot. Add cold water to cover; season with salt. Bring to a boil over medium-high heat. Reduce heat; simmer until vegetables can be pierced with a fork, 20-25 minutes. Drain vegetables well. Pass vegetables through food mill or potato ricer into same pot. Meanwhile, bring cream and milk just to a simmer in a medium saucepan; remove from heat. Stir vegetable purée constantly over medium-low heat until excess moisture evaporates, about 2 minutes. Stir butter into purée a few pieces at a time, blending between additions. Remove from heat; slowly fold in cream mixture until a smooth purée forms. Season to taste with salt and pepper. DO AHEAD: Purée can be made 1 day ahead. Cover; chill. Rewarm in a microwave or in a heatproof bowl set over a large pot of simmering water. Strain hot purée through a medium-mesh sieve into a serving bowl (this makes the texture especially smooth and creamy). Drizzle with oil; scatter hazelnuts over.