Scrub the potatoes and cut into thick slices. Top and tail the green beans, then cut into 2.5 cm lengths; put aside.
Heat the butter and oil in a wide, shallow saucepan or frying pan, over high heat. When it begins to sizzle, stir in the whole green chillies, the cumin seeds, turmeric and garam masala. Peel the garlic and crush it into the pan; stir and fry for 30 seconds.
Add the potatoes to the pan and season with some salt. Stir until coated with the butter and oil.
Stir in the beans, cover the pan, then reduce the heat to moderate and cook for 15 minutes, stirring occasionally. The curry is ready to serve as soon as the potatoes are cooked through.