Combine all dry ingredients. Place water, buttermilk, butter in microwaveable dish and microwave just until lukewarm. Add eggs and whisk into other liquids.
Add liquid ingredients to dry ingredients. It will resemble the texture of a brownie batter. Spray some plastic wrap with nonstick spray and cover bowl. Set aside to rise for about 1 1/2 hours or until almost tripled in volume.
Line a baking sheet with parchment paper.
Sprinkle flour on counter where you will be working. Punch down dough to deflate. Scrape dough onto flour. Work enough flour into dough to form a log shape. Cut into quarters, then cut each quarter into thirds, to get 12 pieces of dough.
Shape into rolls and place on baking sheet as you work. http://www.recipetineats.com/soft-no-knead-dinner-rolls/ has a video for how to shape the rolls. Cover with plastic wrap sprayed with nonstick cooking spray. Set aside and let rise for another 35-45 minutes.
Preheat oven to 390F. Bake rolls for about 18 minutes, or until the rolls are a golden brown and the roll sounds hollow when tapped. Remove rolls from oven and brush with melted butter.