Mix dough ingredients:

In the bowl of a stand mixer, blend together the pineapple juice, milk, melted butter, both sugars, 2 eggs, vanilla, and yeast. Add the all-purpose flour along with 2 cups (286 grams) of the bread flour; stir with a wooden spoon until a shaggy, rough dough forms. Mix in the salt. Fit the dough hook, then run the mixer on medium-low. Slowly add the remaining bread flour only until the dough coheres; depending on your climate and flour brand, you might not need all of it. Knead on medium-high for 4 to 5 minutes, until the dough is soft and smooth.

First rise:

Lightly oil or moisten your hands, then transfer the dough to a gently greased medium bowl. Cover with plastic wrap. Let it rise until puffy and doubled, around 1 ½ hours.

Shape rolls:

Grease a 9x13-inch metal baking pan with cooking spray. Gently press down the dough to deflate. Using a bench scraper or knife, portion the dough into 15 equal pieces. Roll each piece into a ball and arrange in the prepared pan.

Egg wash and second rise:

In a small bowl, whisk the remaining egg with 2 tablespoons of water. Brush this mixture over all the rolls. Cover with plastic wrap and let rise again until doubled, about 1 hour.

Preheat oven:

Meanwhile, preheat the oven to 375°F (190°C).

Bake and butter:

Bake the rolls for 20 minutes, until golden brown. Brush with melted butter. Serve warm. Store leftovers in an airtight container for up to 3 days.