For the puree: Place the potatoes in a pot large enough to accommodate the celery root and the potatoes. Add enough water to cover the vegetables by 2 inches and season generously with salt. Bring to a boil and cook for about 10 minutes. Add the celery root and cook until both vegetables are fork tender. Strain the celery root and potatoes.
Pour the cream in a small saucepan and bring to a boil. Meanwhile, pass the celery root and potatoes through a food mill into a large bowl. Add one-quarter of the hot cream and 2 pats of the butter. Stir vigorously until the cream and butter are thoroughly combined. Repeat for the remaining cream and butter. Taste for seasoning, you will probably have to add salt. Keep warm until ready to use.
For the haricot verts: Bring a large pot of well-salted water to a boil over high heat. Set up a bowl of well-salted ice water for shocking.
Add the beans to the boiling water and cook until tender but still have some bite, 5 to 7 minutes. Strain and immediately transfer the beans to the salted ice water. Once cool, strain and set aside until ready to use.
For the beef: Preheat the oven to 375 degrees F.
Coat a medium saute pan with olive oil and set over medium heat. Add the onions, season with salt and cook until soft and aromatic, 4 minutes. Add the cremini and shiitake mushrooms, and cook until they release some water and then become dry. Add the sherry and cook until almost dry. Remove from the heat and cool. Add the blue cheese, breadcrumbs, chives and parsley, and mix to combine. Transfer the filling to a pastry bag and set aside.
Stick a paring knife into a steak and wiggle it back and forth to make a pocket. Repeat for the remaining steak, then squeeze the stuffing into each pocket. Sprinkle the steaks with salt. Coat an ovenproof pan with canola oil and set over medium-high heat. Sear the steaks on both sides and transfer the pan to the oven for 5 minutes. Remove the steaks from the pan and set aside to rest.
Return the pan to the stovetop and set over medium heat. Add the shallots and season with salt. Cook until soft and aromatic. Add the red wine and reduce by half. Stir in the beef stock and mustard. Bring to a boil, and then reduce to a simmer. Whisk in some butter to finish.
To finish the beans, coat a large saute pan with olive oil. Add the garlic and crushed red pepper, and set over medium-high heat. When the garlic becomes golden and very aromatic, remove it and discard. It has fulfilled its garlic destiny. Add the beans to the pan and saute until hot and coated with oil. Transfer the beans to a serving bowl and season with salt.
Top each steak with some pan sauce and serve with some celeriac puree and beans. Garnish with fresh chives to serve.