Everything-Cheddar Filled Braid

To make the dough: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. Combine the flour with the remaining dough ingredients, and mix and knead — by hand, mixer, or bread machine set to the dough cycle — to make a smooth, very soft dough. The dough will stick a bit to the bottom of the bowl if you're using a stand mixer., Place the dough in a lightly greased bowl, cover, and let it rise for 45 to 60 minutes, or until it's doubled in size., To make the filling: While the dough is rising, stir together the cheese powder, everything topping, water and melted butter. Set aside., Gently deflate the dough and roll it into a 10" x 15" rectangle on a piece of parchment paper. Lightly press two lines down the dough lengthwise, to divide it into 3 equal sections., Spread the filling (reheat it in the microwave, if necessary to make it spreadable) down the center section of the dough, and top with the grated cheese., To form the braid: Cut 1" crosswise strips down the length of the outside sections, making sure you have the same number of strips on each side., Beginning on the left, lift the top dough strip and gently bring it across the filling diagonally. Repeat on the other side with the top dough strip, so that the two strips crisscross each other. Continue down the entire braid, alternating strips to form the loaf., Transfer the braid on parchment to a baking sheet, cover, and let it rise until doubled, 45 to 60 minutes., While the braid is rising, preheat the oven to 375°F., Brush the braid with the egg wash and sprinkle with the everything topping., Bake the braid for 25 to 30 minutes, tenting it with foil after 20 to 25 minutes if necessary to prevent over-browning., Remove the braid from the oven, and transfer it to a rack to cool slightly; it's best enjoyed warm., Store, well-wrapped, at room temperature for a couple of days; freeze for longer storage. Reheat any leftover bread in a 250°F oven for about 10 minutes.