In a small saucepan over medium heat, combine 1/3 cup of bread flour and 1 cup of water, whisking constantly until a thick paste is formed, about 5 minutes. You'll know it's ready when it resembles a smooth pudding. Remove from heat and stir in heavy cream and honey until both dissolve completely.
Transfer the mixture into a stand mixer fitted with a dough hook. Add nonfat dry milk powder, active dry yeast, kosher salt, 2 eggs, and the remaining 5 cups of bread flour. Knead on medium speed for about 5 minutes. The dough should start pulling away from the bowl and feel smooth to the touch.
Incorporate the unsalted butter pieces gradually, mixing one piece at a time until fully integrated. The dough will become shinier and more elastic, which should take about 4 minutes. You want it to be soft but not sticky.
Coat a large bowl with nonstick vegetable oil spray, then place the dough inside and turn it to coat all sides. Cover the bowl with plastic wrap and let the dough rise in a warm place until it has doubled in size, roughly 1 hour. Keep an eye on it, as it will become puffy and magnificent!
Once risen, lightly coat a 6-cup jumbo muffin pan with nonstick spray. Turn the dough onto a floured surface and divide it into 6 equal pieces. Take each piece and divide it further into 3 smaller pieces, creating a total of 18 pieces. Shape them into balls.
Place 3 smaller pieces of dough side by side in each muffin cup. They should be snug but not squished. Cover the pan loosely with plastic wrap and let it rise again in a warm place until doubled in size and puffing over the top, about 1 hour.
Preheat your oven to 375°F (190°C). Beat the remaining egg with 1 teaspoon of water to create an egg wash. Brush the tops of the dough with this mixture and sprinkle with flaky sea salt.
Bake for about 25 to 35 minutes, rotating the pan halfway through. The Milk Bread should turn a lovely deep golden brown. To check for doneness, tap the bottom; it should sound hollow. Let the bread cool slightly in the pan before carefully turning it out onto a wire rack.