Heat vegetable oil in a small skillet over medium-high heat. Add half the shallots and fry until crisp and nicely brown, 1-2 minutes. Using a slotted spoon, transfer to a plate lined with a paper towel to drain. Repeat with remaining shallots. Set aside at room temperature. (Shallots may be cooked several hours in advance).
Heat a large skillet over medium-high heat and add butter and olive oil. When butter is melted, add green beans and saute, stirring frequently, until bright green and crisp tender, about 5 minutes. Season with salt and pepper. Transfer to a serving platter and top with crisp shallots. Serve immediately.