01For dough: Combine flour, water, oil, honey, 2 eggs, yeast and salt in bowl of stand mixer fitted with a dough hook attachment. Mix on medium low speed until smooth and elastic, about 5 minutes. Cover with plastic wrap and let rest until doubled in size, about 1 hour.
02Preheat oven to 375 F and line a rimmed baking sheet with parchment paper. Divided dough into 6 equal pieces. Roll each piece out on a lightly floured work surface into a 10-inch long rope. Roll each rope out 4 inches wide. Fill each rope evenly with cheddar. Roll ropes back together and pinch edges to seal.
03Lay 3 ropes onto prepared baking sheet, and pinch ends together to form a triangle. Weave 3 more ropes over and underneath each point of the first triangle to make a second triangle, pinching ends together to make a 6-pointed star. Cover with plastic wrap and let rise for 30 minutes. Brush star with egg yolk and sprinkle with sesame seeds. Bake until golden brown, about 30 to 35 minutes.
04For cheese sauce: Bring milk to simmer in medium saucepan over medium heat, about 5 minutes. Whisk in cheddar and Monterey Jack until smooth, about 1 to 2 minutes. Remove from heat and serve with challah.