Add the olive oil to a a large saucepan over medium heat for 30 seconds. Add the shallots and green peppercorns and sauté until the shallots have some browning on the edges. Remove from heat and let cool for a minute.
Next, add the water to the slightly cooled pan with the shallots and peppercorns and stir. Then slowly add the brandy, being very careful - if the pan is still too hot the brandy can ignite, so make sure you do this slowly and carefully. Return the pan to medium-low heat and cook for a couple of minutes. After 2 minutes, you can turn the heat to medium and cook until very little liquid remains.
Add the blueberries and stir. Then add everything except for the balsamic vinegar and butter and stir to combine. Cook on medium, stirring every few minutes, for about 30 minutes or until the blueberries have broken down completely. As you stir, you can press the blueberries some to help the process. Once the sauce has cooked for 30 minutes, it will have reduced into a thicker consistency.
Remove from the heat and strain through a fine mesh strainer into a small bowl or container. Wipe the pan free of any chunks that didn’t come out. While the liquid strains from the solids, you can gently press down on the solids with the back of a spoon. Once the juices strain completely. discard the solids and return the liquid to the pan. Bring the reduction back up to warm over low heat and whisk in the butter and balsamic vinegar. Taste and add salt if needed.
Serve over your favorite proteins, like duck, pork chops or a pork tenderloin, a rack of lamb or chicken!