Brew two shots of espresso using your espresso machine or moka pot, ensuring the coffee is hot and aromatic with a rich crema on top. If you don't have an espresso maker, brew a very strong coffee using double the normal amount of grounds. Set the espresso aside while you prepare the other ingredients.
In your tall glass or mug, combine the vanilla syrup, caramel syrup, and white chocolate sauce at the bottom. Stir these syrups together vigorously with a spoon for about 30 seconds until they're well blended and create a smooth, golden-colored base.
If making an iced version, fill your glass with ice cubes until it's about three-quarters full, allowing the ice to chill the glass. For a hot version, skip the ice and proceed to the next step with your warmed mug.
Pour the freshly brewed espresso shots directly over the syrup mixture and ice, watching as the dark espresso swirls through the golden syrups. Stir gently for about 15 seconds to help the syrups dissolve and distribute evenly throughout the espresso.
Add the milk to the glass, pouring it slowly over the espresso and ice mixture until the glass is nearly full, leaving about an inch of space at the top. The drink should take on a beautiful caramel color as the milk combines with the espresso and syrups.
Stir the entire drink thoroughly from bottom to top using a long spoon, making sure all the syrups are fully incorporated and the color is uniform throughout. You should see no separation between layers, and the drink should have a smooth, creamy appearance.
Top the drink with a generous dollop of whipped cream, creating a fluffy cloud that sits just above the rim of the glass. The whipped cream should be thick enough to hold its shape and provide a creamy contrast to the drink below.
Finish by drizzling caramel sauce over the whipped cream in a decorative pattern, allowing some to cascade down the sides of the whipped cream. Serve immediately with a straw and enjoy this indulgent copycat Golden Eagle that rivals the original Dutch Bros version.