Place walnuts in a bowl, cover with warm water, and soak for 2 hours. Drain well.
Preheat the oven to 200 degrees F (95 degrees C). Spread walnuts onto a baking sheet.
Warm the walnuts in the preheated oven until dried completely, about 10 minutes. Increase oven temperature to 375 degrees F (190 degrees C) and toast walnuts until fragrant and lightly browned, 5 to 10 minutes. Remove from oven and cool completely, at least 20 minutes.
Combine walnuts and walnut oil in the bowl of a food processor; pulse until pureed. Pour into a lidded jar and store up to 1 week in the refrigerator.