Activate the yeast. In a large bowl, whisk warm milk with sugar and yeast. Let it sit 5–10 minutes until foamy. If it doesn’t foam, the milk may be too hot or the yeast inactive; try again with fresh yeast.
Make the dough. Add egg and softened butter to the bowl and stir to combine. Add 3 cups (360 g) flour and the salt. Mix until a shaggy dough forms. Knead on a lightly floured surface for 8–10 minutes (or 5–6 minutes with a mixer and dough hook) until smooth and slightly tacky. If it’s very sticky, sprinkle in the additional ¼ cup flour gradually.
First rise. Place the dough in a lightly oiled bowl, cover, and let rise in a warm spot until doubled, about 60–90 minutes. A slightly warm oven with the light on works well.
Mix the filling. Stir the softened butter with garlic, parsley, chives, oregano, red pepper flakes, salt, and black pepper. Combine the cheeses in a separate bowl.
Shape the loaf. Punch down the dough and roll it into a 10×16-inch (25×40 cm) rectangle. Spread the garlic-herb butter evenly, leaving a ½-inch border. Sprinkle all the cheese over the buttered surface.
Roll and swirl. Starting from a long side, roll into a tight log. Pinch the seam. With a sharp knife, slice the log lengthwise to expose the layers. Twist the two long strands together, keeping the cut sides facing up, then tuck the ends. Lift into a parchment-lined 9×5-inch loaf pan.
Second rise. Cover and let rise until puffy and just peeking over the rim, 30–45 minutes. Near the end, preheat the oven to 350°F (175°C).
Bake. Brush with egg wash if using. Bake 35–40 minutes until deep golden and the center reaches about 190°F (88°C). If the top browns too fast, tent with foil for the last 10–15 minutes.
Finish and serve. Cool in the pan 10–15 minutes, then lift out. Brush with a little melted butter and a pinch of parsley if you like. Slice while warm. The cheese will be stretchy, the crust a little crisp, the inside soft. Perfect with soup or on its own, no judgment.