Begin by mixing your warmed milk with the yeast, using a fork to break up as necessary. Allow this to sit for about 10 minutes until nice and bubbly
Go ahead and grease a large bowl for later. (This is also a great time to mix that egg replacer, if not already done)
While you're waiting for the yeast, add the flour, sugar, and salt to a separate stand mixer equipped with a dough hook
Give those dry ingredients a quick whisk to incorporate
Before we start mixing anything else, first remove half of the flour mixture and set aside
Finally, add the egg-replacer, bubby yeast/milk, and butter to the half of the flour mixture still in the stand mixer. Mix on medium-low until mostly smooth (just a minute or two)
Turn off the mixer, and scrape down the sides and bottom thoroughly before we do anything else
Next, with the mixer on low, add the rest of the flour mixture bit-by-bit. (Don't measure or anything, but I'd say in 1/4 cup increments, giving it a bit of time to incorporate before adding more.)
When the rest of the flour has been poured in, ramp the mixer back up to medium-low and allow this to knead for 2-3 minutes until it pulls away from the sides and comes together on the paddle nicely
When nearing the 3-minute mark, if the dough still isn't coming together, simply add dashes of flour (1/2 Tablespoon-ish) bit-by-bit until it pulls away from the sides.
At this point, the dough shouldn't be too sticky, and it should bounce back a bit when poked
Finally, dump out the dough onto a lightly floured surface... Knock it around and lightly roll/knead/shape it into a tight ball with your hands
Place the dough, ugly side down (we still love you), and cover with a damp towel
Allow dough to rise in a warm spot for 1 hour (maybe longer if in a cooler room) until doubled