Combine all in a medium saucepan over medium-high heat.
Bring the mixture to a simmer, stirring occasionally to dissolve the sweetener and starch.
Reduce the heat to maintain a gentle simmer and cook for 2-3 minutes, until the sauce has slightly thickened and some blueberries have burst.
Remove from the heat and let it cool slightly. The compote will continue to thicken as it cools.
Add a pinch of cinnamon, a strip of lemon zest, or a splash of vanilla extract during cooking for an extra layer of flavor.
Cool the compote completely and store it in an airtight container in the refrigerator for up to five days.