In a measuring cup, stir 1/2 cup warm water (about 110F), 1 package active dry yeast and 1 teaspoon sugar until dissolved. Set aside and let stand until bubbly (about 10 minutes).
In a medium saucepan on medium heat, warm 1/2 cup milk until you see bubbles forming at the edges (about 180F). Remove from heat and stir 1/4 cup sugar, 1 teaspoon salt, and 1/4 cup butter until the butter has completely melted.
Set aside and let cool until lukewarm.
In a large bowl, combine your yeast mixture, your milk mixture, eggs and 1 1/2 cups flour. Stir until combined. Proceed to add the rest of your flour 1/2 cup at a time combining well after each addition.
Once the dough starts pulling and sticking together in a ball, transfer it into a lightly floured surface and knead until smooth and elastic (8-10 minutes). When in doubt, knead some more. Careful not to over-flour your dough. You want it elastic but still a little sticky.
Oil a large bowl with 1 tablespoon canola oil. Place your dough in the bowl and turn to ensure the whole dough is coated. Cover with a damp cloth and allow to rise in a dry warm place (about 90F) until it doubles in size (about 1 hour).
In a medium bowl combine 1/2 cup melted butter, 1/2 cup brown sugar and 1 1/2 cups unsweetened shredded coconut. Pour into a greased 9x13 inch baking dish (see notes) and spread evenly on the bottom.
When your dough is ready, transfer it into a lightly floured surface and roll into (roughly) a 12x14 inch rectangle. Brush the dough with melted butter then spread ube jam (see notes), leaving a half inch border around.
Tightly roll the dough (long side up) and pinch the seams to seal. Brush with more melted butter. Cut the roll into 12 pieces (see notes) and place cut side down on your baking dish. Space them out evenly to allow the dough space to rise. Cover and let rise for another 30 minutes.
When your rolls are just about ready, preheat your oven to 375F and bake for 20-25 minutes or until golden brown.
Let the rolls cool slightly in the baking dish before you invert them onto a serving platter. You can also opt to scoop them out one by one. Top with more toasted coconut from the bottom of the dish.
The baking dish you see in the photos is 9x13 inches. I've also baked these in an 8x11 inch dish. The size of pan you use will determine how many rolls you can make. For 8x11, I made 6 giant rolls.
To make ube jam more spreadable, I leave it out on the counter for about an hour before I plan to use it. If it's still too tough, I microwave it for 10 seconds or so to soften it further.
See post for the complete step-by-step photos and more baking tips.