Melt 2 tablespoons of the butter in a 12 inch skillet over medium heat. Add the almonds and sauté, stirring frequently, until they are golden brown, about 2-3 minutes. Transfer to the work bowl of a food processor and set aside.
Add the remaining 2 tablespoons butter to the pan. Once the foaming subsides, add onion, garlic, mushrooms, salt, thyme, and pepper. Cook, stirring occasionally, until the vegetables are soft and the mushrooms are well browned, about 10 minutes. Add the wine and continue to cook until it has evaporated, about 2 minutes.
Process the toasted almonds in the food processor to form a paste, scraping down the sides of the bowl as necessary. With the motor running, add the oil and process until creamy.
Add the mushroom mixture and process until the pâté is smooth. Salt and pepper to taste. Transfer to a bowl, cover and chill for at least 2 hours prior to serving. Serve cool or at room temperature. The pâté will keep for up to 5 days in the refrigerator.