Spiralize celeriac using shredder blade. Take handfuls of spiralized celeriac and cut into manageable lengths with scissors.
Bring a pot of water to a boil. Salt generously; add baby broccolini. Cook until tender, about 5 minutes. Using a fine-mesh sieve or slotted spoon, transfer to a bowl of cold water. Drain. Chop finely. (Do not drain cooking water.)
Heat oil in a heavy skillet over medium heat; add garlic and red pepper flakes. Sauté until garlic is fragrant, 30 seconds to 1 minute. Add broccoli; toss together for 1 minute. Season with salt, remove from heat and keep warm.
Bring water back to a boil and add spiralized celeriac. Cook celeriac for 1 1/2 to 2 minutes. Drain and toss with baby broccoli and cheese.