Heat oil and butter in a large saucepan over medium heat.
Finely chop the onion and add it to the saucepan along with a generous pinch of salt once the butter has melted.
Peel and dice the potato into small cubes, then add them to the onions and cook until they become soft (10-15 minutes).
Mince the garlic, add it to the pot, and fry until it becomes fragrant (about 1 minute).
Keep some peas aside for garnish; soak them in boiling water for 3 minutes, then transfer to cold water and set aside.
Combine peas, vegetable stock, and miso paste in the pot.
Simmer for 5-10 minutes or until the potatoes are fully cooked. Introduce a generous handful of mint leaves and cover the pot with a lid.
Blend the soup until it reaches a smooth consistency. Return it to the pot and bring it to a simmer. Season to taste with lemon juice, salt, pepper, and sugar as needed.
Serve by ladling the soup into bowls and garnishing with a swirl of cream, olive oil, a spoonful of peas, crispy onions, and a sprinkle of smoked paprika.
Toast and butter your sourdough, then enjoy the meal.