In a gallon Ziploc bag, combine water, salt, vinegar, and brown sugar. Mix and dissolve the ingredients, then add both tenderloins. Brine in the refrigerator for 20 minutes (no longer).
Remove the tenderloins from the brine, and dry well.
Preheat oven to 400°F.
Season the tenderloins with Tony Chachere Seasoning on all sides. Heat oil in a skillet on high heat, and sear the tenderloins 2 minutes on 2 opposite sides. Transfer each tenderloin to its own aluminum foil. Top with butter slices and Italian seasoning. Close securely and place on a baking sheet.
Bake 18-24 minutes or until internal temperature reaches 145-150°F. Slightly loosen the foil, and let stand 5-10 minutes.
Carefully drain the seasoned butter to a serving bowl, and slice at a diagonal.