This traditional Japanese-style bread, also known as Japanese milk bread, has a soft, buttery texture unlike traditional American white bread. Martha made this recipe on Martha Bakes episode 606.
Place warm water in a small bowl. Sprinkle over yeast and 1 1/2 teaspoons sugar and whisk to combine. Let stand until creamy, about 5 minutes.
Whisk together 3 1/4 cups flour, salt, and remaining tablespoon sugar in bowl of a standing mixer. Attach dough hook, and mix on low speed adding yeast mixture, milk, and egg. Increase speed to medium and mix until dough comes together, scraping down sides of bowl as necessary. If dough does not come together, add more flour, 1 tablespoon at a time, up to 1/4 cup.
Continue kneading for 10 minutes. Add butter and mix until incorporated and dough is smooth, 5 to 8 minutes. (Dough may come apart before coming back together.)
Meanwhile, butter a large bowl. Turn dough onto a lightly floured work surface and shape it into a ball. Transfer dough to the prepared bowl, turning dough to coat. Cover lightly with plastic wrap sprayed with cooking spray and let stand in a warm place until doubled in bulk, 45 to 60 minutes.
Place dough, top-side down, on lightly floured work surface to deflate. Shape dough into a ball and return to the buttered bowl. Cover lightly with plastic wrap sprayed with cooking spray, and let stand in a warm place until doubled in bulk, 45 to 60 minutes.
Butter a 4 1/2-inch-by-8 1/2-inch loaf pan. Place dough, top-side down, on lightly floured work surface to deflate. Pat dough into a 7-inch square using your hands. Fold bottom edge two thirds of the way up, and fold again so that the top edge meets the bottom edge as you would a business letter. Pat dough a second time into a 7-inch square. Roll dough to form a tight log and pinch to seal. Pat the ends just enough to fit into the pan, and place the dough seam side down into the prepared pan.
Cover with plastic wrap sprayed with cooking spray. Let stand in a warm place until dough has risen about 3 inches beyond the top of the pan and leaves an indentation when gently pressed with a fingertip, 60 to 75 minutes.
Preheat oven to 425 degrees (or 400 degrees for a convection oven) with rack set in the center.
Remove plastic wrap, and spritz surface of dough lightly with water. Transfer to oven and bake for 15 minutes. Reduce oven temperature to 375 degrees (or 350 degrees for a convection oven) and continue to bake until deep golden-brown and an instant-read thermometer registers 190 degrees when inserted into the center of the loaf, about 25 minutes more. If browning too quickly, tent lightly with foil.
Transfer to a wire rack to cool slightly; turn out loaf. Brush top with butter to coat and let cool almost completely before slicing.