In a large bowl or in a stand mixer fitted with a dough hook, stir together the flour, yeast, salt, and sugar. In a small bowl or measuring cup, combine the water, milk, and olive oil and then stir it into the flour mixture.
Knead, either by hand on a lightly floured surface or with the stand mixer on medium speed, adding more flour if needed (I added about a tablespoon more), until smooth, 7 to 10 minutes. Transfer the dough to an oiled bowl, cover it with plastic wrap or a damp kitchen towel, and let it rise until doubled in size, about 2 hours.
Line a baking sheet with parchment paper. Divide the dough into 8 equal parts and keep it covered when you’re not working with it. Working with one piece of dough at a time, roll out a long skinny snake and wrap it firmly and evenly around a hot dog. Roll it back and forth on your work surface a couple of times so that the coils of the dough stick together, and then place it on the baking sheet. Continue with the remaining dough and hot dogs, placing them 1 1/2 inches apart on the baking sheet. Let them rise for 30 more minutes and preheat the oven to 350 degrees F.
Brush the tops and sides evenly with the egg wash and then sprinkle liberally with sesame seeds and za’aatar.
Bake until lightly browned. Begin checking for doneness at 18 minutes.
Let cool slightly and enjoy with lots of ketchup.