Mix sourdough starter, water, and honey in a large bowl or lidded container, then stir in the flours and salt to form a firm dough. Turn onto a floured surface and knead for about 10 minutes, adding flour as needed, until the dough feels elastic but quite stiff. Place the dough back into its container and cover loosely with its lid, plastic wrap or a damp kitchen towel, and allow it to rise in a warm place for approximately 8-12 hours (give or take a few hours, depending on your ambient temperature and other factors) until roughly doubled in size.
Prepare cheesy kale filling: in a large skillet over medium heat, saute the chopped kale and garlic in olive oil until the kale wilts and the garlic is fragrant. Add the vinegar and honey, toss to combine, then remove the pan from the heat. After the cooked greens are cool, mix in the mustard seed powder and cheese, then chill the mixture until the dough is finished rising.
Gently deflate the dough, move to a floured surface and stretch it into a large rectangle about 1 inch thick. Scatter your filling in an even layer all over the surface of dough. Starting from one edge, roll the dough into a spiral, then tuck each end of the roll under the center, shaping the dough into a round. Knead a few times to more evenly distribute the filling, then divide the dough into 8 equal pieces.
Continuing to work on your floured surface (and sprinkling more flour as needed), form each piece of dough into a ball, creating gentle surface tension by stretching each of the four sides of the dough down to the bottom of the ball. Then, pierce the center of each ball with your thumb and gently stretch the hole to about a 1.5 inch diameter. Place the shaped bagels onto a floured sheet pan, cover with plastic wrap, and refrigerate overnight (or up to 24 hours).
When ready to bake, preheat oven to 420 F and prepare a large sheet pan by topping it with parchment paper, and sprinkling it with a layer of any seasonings that will be used to top the bagels. Put water in a large pot over high heat to boil, and when the water has boiled, add the baking soda (be careful, it will foam). Carefully drop each bagel, 2 or 3 at a time, into the water and boil for 1 minute before flipping, then boil on the second side for 1 minute more. Use a slotted spoon to transfer the bagels onto the prepared sheet pan, then top with your choice of seasonings. After all bagels are boiled, make sure they all have a chance to dry for 5 minutes before baking to avoid a gummy texture. Bake for 25-30 minutes, until they are brown and sound hollow when tapped.