Combine the dry ingredients (bread flour, salt, instant yeast, and white sugar) in a large mixing bowl.
In a separate bowl, beat the egg into the whole milk until blended.
Add the milk-and-egg mixture to the dry ingredients. Add the cold water and mix until the dough ingredients are evenly hydrated (if needed, add the water gradually so the dough comes together).
If using a mixer or stand mixer: start with the lyre/flat beater (or paddle) on low speed (speed 2) and mix for 3 minutes to incorporate. Switch to the dough hook and knead on medium-low (speed 2) for 5 minutes. Cover the bowl with a cloth and let the dough rest 3 minutes. Add the butter (100 g) and knead on medium-low (speed 2) for 5 minutes, until the dough is smooth and elastic.
If kneading by hand: turn the dough onto a lightly floured work surface and knead until well incorporated and the dough feels smooth and silky (this may take up to 10 minutes). You may knead 5 minutes, cover and rest 5 minutes, then continue. When the dough is firm and no longer sticky, add the butter in pieces and knead until smooth and silky again, about 5–8 minutes.
Shape the dough into a ball. Cover it with a cloth and let it rise in a cool, draft-free place until it doubles in size (about 30–90 minutes; times vary).
Turn the risen dough onto a lightly floured surface and shape it into a rectangle. Place the rectangle on a tray, cover with plastic wrap, and refrigerate for 10 minutes.
Remove the dough from the refrigerator. With a rolling pin, roll the dough into a rectangle about 1/4 inch (5 mm) thick. Fold the dough over itself, rotate it 90°, roll again, and fold again. Repeat this roll-and-fold sequence 2–3 more times (total 3–4 folds).
Divide the dough into 10 equal portions (weigh portions if you want exact sizes).
To make round loaves: flatten each portion and pull the edges toward the center to form a tight ball; place the seam side down and cup your hand around the dough to roll it into a smooth surface. To make elongated buns: flatten each portion into a rectangle and roll from the top edge to the bottom edge, pressing the seam to seal.
Place the shaped buns on a baking tray with a small space between them. Cover with a clean towel and let them proof until doubled in size, about 20–45 minutes.
When the buns are nearly doubled, preheat a conventional oven to 350°F (180°C).
Once the loaves have doubled, bake in the preheated oven until golden brown, about 18–22 minutes.
Remove the bread from the oven and cool for a few minutes on a rack.
Serve warm. Store covered with a clean cloth to serve within a few hours, or refrigerate and reheat in a toaster to serve the next day.