Melt the butter in a saucepan over medium heat. Whisk in the flour and stir for about 1 minute until bubbly and golden brown. Gradually whisk in the milk until smooth. Bring to a simmer while stirring occasionally. Once the sauce starts to thicken, add in the cheese and whisk until smooth with no lumps. The sauce should be thick and creamy.
Heat a saute pan on medium heat. Once hot, add the oil. Saute the onion until golden brown.
Heat a grill or grill pan on medium heat. Grill the hot dogs, turning occasionally, so all sides are golden brown.
Place the hot dogs on the bun, drizzle with cheese sauce, top with onions.