In a large bowl, beat the butter and cream cheese until well-blended and smooth. Add the cheddar, egg yolk, flour and salt and beat on low speed with the paddle attachment of your stand mixer or stir by hand until the dough comes together. Turn it out onto the countertop and knead a few times, then divide in half, shaping each half into a disc, and let sit for 20 minutes or wrap and refrigerate for up to 3 days.
When you’re ready to bake, preheat your oven to 350F. On a lightly floured surface, roll each piece of dough out into about a 12-inch circle (the dough should be about 1/8-inch thick). Sprinkle with everything bagel seasoning and Parmesan (if you like) and roll gently so that it adheres to the dough (and sinks into it a bit).
Cut each circle into quarters, then cut each quarter into 3 wedges, making 12 wedges out of each disc. Roll each wedge up like a crescent roll and place on a parchment-lined baking sheet. If you like, brush with a little beaten egg or cream (which will make it more golden and glossy) and sprinkle with a bit more of the everything bagel blend.
Make for 15-20 minutes, or until golden and set. Makes 2 dozen rugelach.