For the carrot butter: Juice the carrots using a juicer (you should have 4 cups/1liter). If you don't have a juicer you can use store-bought carrot juice.
Bring the carrot juice to a simmer in a small saucepan. Cook over low heat until reduced to 1 cup (250 ml), about 45 minutes. Add the diluted cornstarch. Slowly add the melted butter, using a hand mixer or whisk to incorporate it. Season with salt and pepper.
For the risotto: Heat the vegetable stock in a saucepan.
In a large skillet, heat the oil and saute the celeriac, parsley roots, parsnips, salsify and shallots. Add vegetable stock, one ladle at a time, stirring constantly with a wooden spoon and cooking until almost all the liquid has been absorbed before adding more. Continue cooking and adding stock until the vegetables are cooked but still al dente, about 25 minutes. Stir in the butter, Parmigiano-Reggiano, chives and parsley. Season with salt and pepper. Keep warm.
Preheat the oven to 400 degrees F (200 degrees C).
For the mushrooms: Heat the oil in a skillet over medium-high heat. Saute the mushrooms until golden brown. Season with steak spice. Transfer the skillet to the oven and roast the mushrooms for 5 minutes.
To serve, divide the vegetable risotto among dishes and top with the mushrooms. Drizzle with carrot butter and garnish with micro herbs.
Heat the oil in a large stockpot over medium heat. Lower the heat and add the carrots, celery, garlic, onions, parsley roots and leeks. Cook until the vegetables are slightly colored, about 5 minutes. Stir in the ketchup, peppercorns, celery leaves and parsley leaves. Add enough water to cover. Bring to a boil, then lower the heat and simmer for 30 to 45 minutes (it's important not to cook it for too long). Strain, cool and refrigerate until ready to use.