Preheat the oven to 220 degrees Celsius/ 430 degrees Fahrenheit.
Prepare vegetables: If using organic onions, carrots, and parsley roots, you don't have to peel them; just wash them well. Quarter the onions. Chop the peeled celeriac, carrots, parsley roots, tomatoes, and bell peppers into large chunks of roughly similar size. Place them on two baking trays lined with baking paper, divide the olive oil between them and mix everything well.
Roast for about 45-60 minutes, stirring every 15 minutes, until the veggies are soft and starting to brown around the edges.
Simmer: When ready, place all the vegetables in a very large pot and add the water and all other ingredients. Bring to a boil, turn the heat down and simmer, uncovered, until reduced by half. It takes between one and a half and two hours.
Strain through a fine-mesh sieve and again through a fine, clean cloth if you wish the broth to be free of every residue.
Reduce: Place in a clean pot, bring to a boil again and add salt and pepper to taste.
Store: Fill in clean jars or bottles while very hot. Put the lid on, let cool, and keep in the fridge. Or you can leave it in the pot until cold, fill it in smaller containers and freeze.
Hazelnut dumplings: whisk the very soft butter and the eggs until frothy. Add the hazelnuts, breadcrumbs, lemon juice, nutmeg, and salt to taste and mix well. Leave to stand for about 10 minutes. Form small balls about the size of a walnut.
Cook dumplings: Bring about 1 liter/ 4 cups vegetable broth to a boil, turn the heat down and simmer the hazelnut dumplings for about 6 minutes.
Adjust the taste with salt, pepper, and some lemon juice.