Add oil & butter to a pan, heated over medium heat.
Add onions & cook for 2-3 minutes, stirring periodically.
Add salt, stir & cook for an additional 2 minutes; then add flour & cook for 1 minute.
Add beef stock & cook until almost fully evaporated & onions have taken on a much darker colour, approximately 12 minutes. They should be really soft & sticky.
Heat another frying pan or skillet over high heat, until smoking and add sausage.
Cover pot to trap smoke, shaking pan occasionally, to evenly colour sausage; until fully heated through.
Pour caramelized onions over sausages, top with cheese & cover pot until cheese fully melts.
Assemble dogs & serve.