Step 1: Combine the bread flour, sugar, yeast, and salt in the bowl of a stand mixer.
Step 2: Add the warm milk and eggs, mixing on low speed until a shaggy dough forms.
Step 3: Knead the dough on medium speed for 8 minutes until smooth and elastic.
Step 4: Add the softened butter one tablespoon at a time, mixing well after each addition until the dough is silky.
Step 5: Transfer the dough to a greased bowl, cover, and let rise in a warm place for 1.5 hours.
Step 6: Punch down the dough and gently fold in the peach slices, being careful not to crush them.
Step 7: Shape the dough into a loaf and place it into a greased 9x5 inch loaf pan.
Step 8: Cover and let rise for another 45-60 minutes until it reaches the top of the pan.
Step 9: Preheat your oven to 375°F (190°C) and brush the top of the loaf with the prepared egg wash.
Step 10: Bake for 25-30 minutes until the Peach Brioche is deep golden brown and sounds hollow when tapped.