In the stand mixer bowl combine the pineapple juice (room temperature), warm 1/2 cup milk, melted cooled butter, 2/3 cup sugar, 2 room-temperature eggs, vanilla, and instant yeast; stir briefly with a fork to combine.
Fit the mixer with the dough hook and add 2 cups of the bread flour and the salt. Mix on the lowest speed until the flour is incorporated.
Add 2 more cups of bread flour and continue kneading, increasing the mixer speed after the flour is incorporated.
For the remaining flour, add up to 1/2 cup more 1/4 cup at a time until the dough is soft and slightly sticky. Knead the dough for 5–6 minutes more; it should clear the sides of the bowl but may cling slightly to the bottom.
Turn the dough onto your hands or a clean surface briefly, spray the mixer bowl with cooking spray, return the dough to the bowl, cover with plastic wrap, and let rise in a warm place until doubled, about 90–120 minutes.
Grease a 9x13-inch baking dish with cooking spray.
Punch down the risen dough lightly, turn it onto a clean counter, and divide into 15 equal pieces using a bench scraper or knife. Roll each piece into a smooth ball.
Place the rolls in the prepared baking dish in 3 rows of 5 so they touch each other. Cover with plastic wrap and let rise until nearly doubled, about 60–90 minutes.
About 20–30 minutes before the end of proofing, preheat the oven to 375°F (190°C).
Whisk together 1 egg and 2 tablespoons milk to make an egg wash. Gently brush the tops of the rolls with the egg wash.
Bake the rolls in the preheated oven for 18 minutes, or until the tops are golden brown.
Remove the pan from the oven and cool the rolls in the pan on a wire rack for 10–15 minutes before serving; optionally brush with butter while still hot for extra shine.