Heat oil and butter in a pot over medium heat until the butter has melted. Add in the garlic and stir constantly for 1 minute until fragrant. Add in the sliced mushrooms and stir-fry until the mushrooms are lightly browned and have reduced in size - about 5 minutes.
Add in 75 ml of the milk and bring to a boil, then turn down the heat and simmer for another 3 minutes, stirring occasionally. Dissolve the corn flour in the remaining milk and drizzle it into the sauce, simmering for another 2 minutes or until the sauce has thickened. Season with salt and black pepper to taste.
Serve immediately over the cooked steaks. If not, cover and heat up when needed.
NOTES
If you do have cream available, you can substitute milk with cream. Omit the cornflour.