In a small saucepan, heat pineapple juice, 1/2 cup water, butter, and 1 tablespoon sugar to between 105° F and 115°F. Sprinkle the yeast over this mixture and allow to sit undisturbed for 5 minutes.
In the bowl of a stand mixer, fitted with a paddle beater, beat the eggs with 3/4 cups sugar. Add the pineapple juice mixture, ginger, and vanilla.
Sift 3 cups flour and salt. Put 3 cups flour in a separate bowl that fits the stand mixer, and still using the paddle beater, slowly add the egg mixture to the flour. Mix until well combined, scraping down bowl as necessary. Sift and add the remaining 3 cups flour and mix thoroughly, changing to dough hook when necessary. Continue to beat on low for 8 minutes, stopping to scrape down bowl as necessary. Dough will be soft and sticky.
Lightly spray a bowl with cooking spray. Transfer dough to bowl, cover, and set in a warm place to rise until doubled, about one hour.
Remove dough from bowl and place onto a lightly floured mat. Knead in 1/2 cup flour, turning and kneading dough about 20-25 times.
Shape into 2 oz. rolls or place dough in greased and floured loaf or cake pans. Cover with a light towel and let rise in a warm place for one hour.
Mix 1 egg with 2 T milk and brush top of rolls.
Bake at 350° for 25-30 minutes, or until tops are light brown. Remove from pans and let cool completely on wire rack.