Warm olive oil in large skillet over medium heat. Add walnuts and cook, stirring occasionally until lightly golden brown—about 5 minutes. Sprinkle with salt and remove from heat.

Place honey, brown sugar, milk, and butter in a large saucepan. Bring to a boil. Boil for five minutes, stirring frequently, reducing heat to prevent from boiling over as needed. Remove from heat, stir in vanilla extract. Cool for 5 minutes then pour over nuts. Store in a jar in the refrigerator, but serve at room temperature. Keeps indefinitely.