For the flour paste: Add 1/2 cup water to a small saucepan set over medium-low heat. Add the flour and cook, whisking constantly, until the mixture is a smooth pudding-like consistency, 30 to 45 seconds. Let cool.
For the dough: Add the milk and egg to the flour paste and whisk together until smooth. Transfer the paste to a stand mixer fitted with a dough hook and add the flour and yeast. Mix on low speed until all the flour is moistened, 1 to 2 minutes. Let rest in the bowl for 15 minutes.
After 15 minutes, with the mixer running on medium-low speed, add the sugar and salt and mix for about 5 minutes. Add 4 tablespoons of the butter and mix, scraping down the sides of the bowl when necessary, about 5 minutes longer. Transfer the dough to a lightly floured surface and knead briefly to form a ball. Spray a mixing bowl with cooking spray, add the dough ball, cover with plastic wrap and let rest until doubled in size, about 1 hour.
Transfer the dough to a work surface and press gently but firmly to release the air. Stretch the dough to form a 9-by-10-inch rectangle. Cut the dough lengthwise into 4 equal strips, then cut those strips into 3 equal pieces. Working with one piece at a time, stretch and press each one into an 8-by-2-inch inch strip. Roll each strip small end to small end in order to form a snug roll.
Grease a 12-inch cast-iron skillet with butter and arrange the rolls in the skillet, 10 around the outside and 2 in the middle. Cover with plastic and let rise until doubled in size, about 45 minutes.
Position an oven rack in the lowest position and preheat the oven to 375 degrees F.
Brush the rolls with the remaining 3 tablespoons butter and bake until golden brown, about 25 minutes. Let cool 5 minutes.
When ready to serve, using a 2-ounce ice cream scoop, place scoops of the garlic-herb or honey butter in the center of the bread and let your guests pull apart the bread from the skillet.