Combine the bread flour, instant yeast, sugar, and salt in a large mixing bowl.
Add the warm milk, Greek yogurt, and vanilla. Mix until a shaggy dough forms, then knead for about 5 minutes until the dough begins to become smooth.
Add the softened butter 1 tablespoon at a time, kneading well after each addition. Continue kneading for 8 to 10 minutes, until the dough is glossy, elastic, and slightly tacky but pulls cleanly from the sides of the bowl.
Place the dough in a lightly greased bowl, cover, and let rise in a warm place for 1 1/2 to 2 hours, until doubled in volume.
Gently deflate the dough and divide it into 8 equal portions. Shape each portion into a smooth ball and arrange the balls in a greased 9 x 5-inch loaf pan.
Cover the pan and let the dough rise for 45 to 60 minutes, until noticeably puffy and about 1 inch above the rim. Preheat the oven to 350°F near the end of the rising time, then stir together the milk and maple syrup and brush it over the loaf.
Bake for 30 to 35 minutes, until deeply golden and the center reaches about 190°F. Cool in the pan for 10 minutes, then transfer the loaf to a rack and cool before slicing.
