Serve this compote with our Citrus-Ricotta Cheesecake.
Cut peels from citrus; cut peels into very thin strips. Set aside. Cut pith from citrus. Working over a bowl to catch fruit and juices, cut fruit segments from membranes. Squeeze juice from membranes into bowl. Pour 1/4 cup juice through a fine sieve into a small bowl; set aside.
Bring a medium saucepan of water to a boil. Add peels; boil 1 minute. Drain; set aside. Bring sugar, 1/4 cup water, and vanilla bean to a boil in a clean medium saucepan over medium-high heat, stirring until sugar is dissolved. Reduce heat to low. Add reserved juice, peels, and the salt; cook 2 minutes. Let cool completely.
Discard vanilla bean. Toss syrup with reserved fruit.
The compote can be covered and refrigerated up to 2 days.