Heat oil in a large pot over medium heat. Cook and stir onion, garlic, galangal, ginger, garam masala, paprika, and chile powder in the hot oil until onion is browned, about 10 minutes.
Stir potatoes, peaches, tomato, butter, fennel leaves, and oregano into the pot; bring to a simmer. Stir in lemon juice. Reduce heat to medium-low; add chicken stock, coconut milk, fish sauce, basil, mint, salt, and pepper. Simmer until potatoes are tender, 25 to 30 minutes.
