Preheat the oven to 350 degrees F.
Divide the vegetable oil and shallots evenly among 4 oven-proof wide-mouthed ramekins. Gently crack 2 eggs per ramekin. Divide the tomato, butter, and cream evenly among the ramekins. Season with salt, and pepper, and put in the oven for approximately 8 to 10 minutes, until eggs whites have set.
Carefully, remove the ramekins from the oven and garnish with fresh sliced chives and serve immediately with toast.