Drain 1/2 cup pineapple juice from the can of pineapple tidbits. Place 1/4 cup flour, 8 tablespoon melted butter, pineapple syrup, and sugar in the bowl of an electric stand mixer.
Place the bread hook on the mixer and mix the ingredients for 10 seconds. Then sprinkle the dry active yeast over the top. Allow the mixture to rest for 10-15 minutes. It should look very foamy. (The liquid will absorb the yeast on its own.)
Mix in 2 eggs, salt, and vanilla. Then with the mixer running on low, slowly add in the remaining flour. Leave the mixer running for 6-8 minutes to knead the bread dough.
Drizzle 1 tablespoon melted butter around the edges of the bowl so the dough doesn't stick, and cover the bowl tightly with plastic wrap. Place in a warm spot and allow the dough to rise until doubles in size. (Usually 90-120 minutes.)
Meanwhile chop the pineapple tidbits into fine pieces and measure out 1/2 cup. Prepare 1/2 cup each of shredded carrot, shredded coconut, and finely chopped macadamia nuts.
Once the dough has doubled in size, turn the mixer on low and mix in the pineapple, shredded carrot, shredded coconut, and macadamia nuts.
Grease and flour two standard 9x5 bread pans. Cut the dough into two equal pieces. Roll each piece into a log and place in the bread pans. Then use the last tablespoon of melted butter to brush the tops of the loaves, so they don't dry out.
Preheat the oven to 350 degrees F. Cover the loaves with plastic and place in a warm place to rise. They need to double in size again to fill the pans and rise above the edge of the rim. (About 45-60 minutes.)
Whisk the egg white with 1 tablespoon of water. Remove the plastic and gently brush the eggwash over the tops of the loaves. Bake for 35-45 minutes, until the tops are golden brown.
Cool in the pans for 10 minutes, then gently flip the loaves out onto a cooling rack to cool the rest of the way. Once the bread is room temperature, wrap well in plastic until ready to serve.
NOTES: This is a heavy buttery dough so it doesn't rise as quickly are regular yeast dough; plus the chunks can make it even more difficult for the dough to rise. However, it must at least double in size, twice, to have a soft airy texture.If your kitchen is cool or drafty, place the dough in a warming drawer to rise. Some ovens have a "proofing" function that keeps the oven at 100 degrees for dough. If you don't have either, you can set your oven to 180 degrees, keep the dough covered in plastic, and proof in the oven for 20-30 minutes. If you go much longer at this temperature the dough will start to dry out.