Preheat the oven to 400 degrees. In a large pot, bring the beans and 6 times their volume of water to a boil over a high flame. Reduce to a simmer and cover. Cook for 30 minutes, stirring occasionally. Add the celeriac and cook until both are completely tender, about 15-20 minutes. In a large mixing bowl, toss together the asparagus, mushrooms and garlic along with the herbs, 1 Tbsp. oil and a pinch of salt. Spread in an even layer on a lightly oiled baking sheet and place in the oven. Roast until slightly browned, turning once, about 10-12 minutes. Meanwhile, lay the slices of bread on a separate baking sheet and place in the oven for 2-4 minutes, turning once, until slightly toasted on each side. Set aside.
When the beans and celeriac are cooked, strain and purée using a food processor or hand blender. While puréeing, slowly add the remaining oil along with a pinch of salt and pepper until shiny and smooth. Spread each piece of toast with the purée and place on 4 plates. Top evenly with the roasted asparagus, mushrooms and radish. Season with a pinch of salt and pepper to taste.