In a small saucepan, combine the 5 tablespoons of water, 5 tablespoons of whole milk, and 3 tablespoons + 1 teaspoon of flour. Whisk to combine.
Place over medium high heat and continue whisking until thickened into a paste (about 5 minutes), being careful not to brown the paste. Remove from the heat and reserve.
In the bowl of a stand mixer with a dough hook attachment, combine the additional flour, white sugar, salt, dry milk powder, instant yeast, warmed milk, melted butter and eggs.
Scrape the reserved Tangzhong Starter into the stand mixer dough as well.
Mix on medium speed for about 3 minutes, or until a rough dough is formed.
Remove any dough sticking to the hook and cover the mixing bowl with a tea towel.
Place the bowl somewhere warm and let sit for 20-25 minutes to rest.
After resting, place the bowl and the dough hook back on the stand mixer.
On medium high speed, knead the with the dough hook for about 2 minutes, until the dough is smooth & forms a nice ball.
Take a large mixing bowl & lightly grease with vegetable oil. Place the dough ball into the oiled bowl, then cover with a tea towel.
Let the dough rise for about 60 minutes in a warm environment, until it has doubled in size (and until pressing with your finger makes a permanent dent).