Place the water, vegetable stock pot, ginger and garlic in a pot and bring to boil over high heat. Reduce the heat to medium low and simmer until fragrant.

Melt 1 tbsp butter in a pan over medium heat. Add mushrooms, soy sauce and 1 tbsp miso and cook until browned, breaking up the miso with spoon. Add the remaining 1 tbsp butter and continue cooking until mushroom are tender and are deeply browned all over. Set aside.

Remove and discard the ginger and garlic from the broth. Remove a ladleful of broth from pot and transfer to a liquid measuring cup. Set aside.

Return the remaining broth back to boil. Add the eggs and cook for 6 to 8 minutes (6 for the runniest yolk and 8 for slightly firmer yolks) remove the eggs and plunge into an ice bath. Peel and set aside.

Return the broth to a boil. Add udon and frozen peas and cook until both are tender, 5 minutes. Remove from the heat. Whisk the remaining 1 tbsp miso into reserved ladleful of broth until smooth. Add the pot and stir to combine.