First dry your salmon with paper towels so that it won't stick to the pan.
Heat oil and butter in a skillet over a medium-high heat.
When butter and oil start to sizzle, add salmon, skin side down. Press with your spatula so that the skin will cook evenly. Cook for 3 minutes.
Then flip and sear the top for 2 minutes more. If your salmon is thick, it may need another minute.
Transfer salmon to a plate and set aside.
Wipe the pan clean and make your sauce in the same pan.
First bring your wine to a simmer and reduce by half the volume. This will take about five minutes. Then add garlic, salt, pepper, and lemon juice.
Whisk in cream and add the cold butter, one tablespoon at a time. As soon as all the butter is whisked in, stir in your capers and turn off the flame.
Pour over your salmon and serve.