Combine the pineapple juice, milk, melted butter, granulated sugar, and brown sugar in a medium bowl. Whisk until the sugars have dissolved. Add the eggs and vanilla and whisk until combined.
In a large bowl, whisk together the instant yeast, bread flour, all-purpose flour, and salt.
Pour the wet ingredients into the dry ingredients and stir with a wooden spoon or rubber spatula until a shaggy dough forms.
Turn the dough out onto a lightly floured surface and knead for 5-7 minutes, until the dough is smooth and elastic. Add more flour as needed if the dough is too sticky.
Place the dough in a lightly greased bowl, cover, and let rise for 1 hour, or until doubled in size.
Punch down the dough to release any air bubbles. Divide the dough into 12 equal pieces (about 2.5 ounces each).
Shape each piece into a smooth ball and place in a greased 9x13 inch baking pan. Cover and let rise for 30 minutes.
Preheat the oven to 350°F (177°C).
In a small bowl, whisk together the egg and water for the egg wash. Brush the tops of the rolls with the egg wash.
Bake for 20-25 minutes, until the tops are golden brown.
Remove from the oven and brush the tops with the melted butter.
Serve warm.
