Make the Dough: In a stand mixer bowl with the dough hook attached, combine the heavy cream, milk, egg, sugar, flour, yeast, and salt in that order.
Knead: Set the mixer to the lowest speed to bring the dough together. Once combined, continue mixing at low speed for 15 minutes, pausing to scrape the bowl as needed. The dough should feel slightly tacky. If overly sticky, add extra flour 1 tablespoon at a time until it pulls away from the bowl. (If mixing by hand, stir ingredients in a bowl, then knead for 20 minutes until smooth and stretchy.)
First Rise: Shape the dough into a ball and place in a bowl covered with a damp towel or overturned plate. Let it rise in a warm area until doubled in size—this will take 1 to 2 hours depending on your kitchen environment. (Tip: a microwave with a mug of hot water creates a great warm space.)
Degas and Divide: Punch the dough down in the bowl to release air. Butter two 9x5-inch loaf pans (or two 9-inch round pans if making buns). Place the dough on a floured surface and divide it into 6 even portions for loaves (about 180g each) or 16 pieces (about 65–70g each) for buns.
Shape: For loaves, roll each of the 6 pieces into a 4x8-inch rectangle and roll tightly into a cigar shape. Place 3 cigars seam-side down in each loaf pan. For buns, roll each piece into a ball and arrange 8 per round cake pan, spaced evenly.
Second Rise: Cover the pans with a towel and let rise again for 1 hour at room temperature.
Bake: Preheat oven to 350°F and position a rack in the center. Brush risen dough with egg wash. Bake for 22 to 24 minutes, or until tops are golden.
Finish: Once out of the oven, immediately brush tops with sugar water for shine and a touch of sweetness. Move bread to a wire rack to cool.