To prepare the noodle dough: in a large mixing bowl, with clean hands, combine the flour, egg and salt, and knead for 10 minutes. If too dry, add a little water; you shouldn’t need more than a teaspoon or so. Form into a ball, cover the bowl with cling wrap, and rest for 30 minutes.
To make the soup: in a round-bottomed wok, fry-pan or skillet over medium-high, heat a tablespoon each of olive oil and butter, fry the onions until soft and translucent, add half the chopped garlic, combine and fry until fragrant. Transfer to a soup pot/Dutch oven.
To the wok/pan, heat another tablespoon each of olive oil and butter, turn heat to high, and fry the mushrooms until brown, add remaining garlic and stir-fry until fragrant, add a pinch of salt, then transfer to a dish and set aside.
To the soup pot/Dutch oven containing the onions and garlic, add one litre of boiling water (or stock of choice or combination of water and stock), then add the diced potatoes and carrots, bay leaves, salt, white pepper, spices, and half the dill, and bring to a boil.
Add another litre of water, bring to a boil again, then reduce to low, add the mushrooms, taste and adjust the seasoning and spices to your palate, then leave to simmer on low heat.
To make the noodles: sprinkle your work surface with flour, divide the dough into four balls, working with one at a time (leave the others under cling wrap), roll the dough into a thin sheet, forming it into a rough rectangular shape, then dust a little flour across the sheet.
Using a knife, working from one side of the dough sheet to the other, starting at a top corner, cut a long thin strip of dough about 5mm in diameter to create a noodle. Repeat until you’ve sliced the whole sheet of dough into noodles.
Sprinkle a large tray with flour, dust your hands in flour, then working with one noodle at a time, holding each end between your two hands, gently pull the noodle a little, stretching it to near breaking point. (Don’t worry if it breaks.)
Hold a noodle from a tip so the rest hangs down, wrap a flour-dusted hand around the top of the noodle and gently slide your hand down so the noodle is lightly covered in flour, then spread the noodle out onto the tray. Repeat with all noodles made so far.
Repeat the three noodle-making steps above with the remaining balls of dough then leave the noodles to dry until you're ready to eat.
Just before you’re ready to eat, turn the heat up to bring the soup to a boil again and add the noodles. They will only take a few minutes to cook, so take care not to over-cook them.
Ladle the mushroom noodle soup into bowls, grind more cracked black pepper on top, garnish with fresh fragrant dill, and spoon a dollop of sour cream onto each bowl.