Make the dough: Combine 3/4 cup warm water (approximately 110 degrees F),the yeast and a pinch of sugar in a large mixing bowl and let sit until foamy, about 10 minutes.
Add 3 eggs and whisk to combine. Add half of the bread flour and beat with a wooden spoon until good and thready, about 3 minutes. Add the butter, the remaining 3 tablespoons sugar, the remaining flour and the salt and mix well. The dough will be a little sticky. Let rest 15 minutes.
Knead the dough to develop the gluten until it feels tight and smooth, about 5 minutes. Transfer the dough to a lightly buttered bowl, cover and let it rise for 1 hour at room temperature. Then chill in the refrigerator,1 to 2 hours or overnight.
Remove the dough from the refrigerator and divide it into 8 even portions. Roll each one into a ball and leave on the counter, covered loosely, to warm up, about 30 minutes.
Meanwhile, make the filling: Heat a large skillet over medium-high heat. Add the beef, season with 3/4 teaspoon salt and 1/2 teaspoon pepper and cook, breaking up the beef, until lightly browned, about 5 minutes. Use a slotted spoon to transfer it to a bowl.
Drain and discard all but a film of the fat from the skillet. Add the butter; when it has melted, add the onion. Cook over medium heat, stirring occasionally, until light golden brown, about 15 minutes. Add the garlic, thyme and rosemary and cook 3 minutes. Add the mixture to the bowl containing the beef.
Without cleaning the skillet, add 1 tablespoon canola oil. Saute the spinach over high heat until wilted and the excess liquid has evaporated, about 1 minute. Chop the spinach, then add it to the beef mixture and set aside to cool.
Roll out the dough: Flatten a dough ball on a heavily floured surface and roll out into a 3-by-5-inch rectangle. Then make wrapping flaps from the four corners of the rectangle by rolling out each corner thinly so you have a thick rectangle with four thinner triangular wings at the corners.
Fill the runzas: Spoon 1/2 cup of the beef filling into the center of the dough rectangle and wrap the flaps over it, pinching to close. Flip the bundle over in your hands, gently forming the runza into a fat football shape. Set the runza seam-side down on an oiled baking sheet. Repeat with the remaining filling and dough balls, arranging them on 2 oiled baking sheets. Let the runzas rise about an inch, uncovered, about 45 minutes. Meanwhile, preheat the oven to 375 degrees F.
Whisk the remaining egg and 2 tablespoons water to make an egg wash and brush it thinly over the tops of the runzas. Bake until golden brown, 25 minutes. Serve hot.
Photograph by Christina Holmes
Recipe courtesy Amy Thielen for Food Network Magazine