In a medium saucepan, combine the cranberries, sugar, orange juice, sea salt and sage leaves. Bring to a boil, then reduce to a simmer. Simmer for 10 minutes, stirring occasionally, until berries have broken down and the sauce has thickened and turned jammy. Remove from heat and discard the sage leaves. Set aside until ready to use. (This step can be prepared ahead.)
Heat the water until warm to the touch, around 110ºF. In the bowl of a stand mixer fitted with the whisk attachment, combine the water, eggs, sugar, vanilla extract and yeast. Switch to the paddle attachment and add the flour, kosher salt, nutmeg and orange zest. Mix until just combined. Switch to the dough hook and knead the dough on low speed for about 3 minutes. The dough will be sticky — this is perfectly fine.
Increase the speed to medium and add the butter to the mixture, one cube at a time. Once all the butter has been added, mix the dough on high speed for 7-10 minutes, until completely smooth and elastic. To test the dough’s readiness, try stretching a piece of it. It should stretch easily to a point where it becomes translucent but doesn’t rip.
Line two baking sheets with parchment paper. Dust the paper well with flour. Tip the cold dough onto a lightly floured work surface and roll it into a 9 1/2 x 12 1 ⁄2-inch rectangle. It should be about 1/2-inch thick.
Use a knife or a chopstick to poke a hole into one side of each doughnut. Be careful not to poke through to the other side. Insert the tip of the pastry bag into the hole and gently squeeze to fill.
Top with powdered sugar. Serve immediately. Yields 12 donuts.