Savory Sourdough Brioche

I forgot to post this recipe after New Years Eve. I wanted to make a special sourdough bread for my friend Jade. I looked at a bunch of recipes online and then sort of made this one up.
Ingredients: Fed sourdough starter (I used about 2 cups that I kept on the counter feeding for about a week so it would get “extra sour-y”)
2 t. sugar
2 t. salt
1 c. milk product (I used a combination of heavy cream and Keffir)
2 eggs
1 stick butter melted on the back of the warm stove
Put all ingredients except flour into stand mixer. Mix until well incorporated. Slowly add flour 1/2c at a time, mixing well after each addition, until dough starts to pull away from the sides of the bowl or your stand mixer starts to get cranky at you because it’s too thick to mix.
Turn out onto floured surface and continue to knead, incorporating more flour, until dough is no longer sticky. It’s been described to me that when you touch the dough it should feel like a “the side of a soft woman’s breast.”
Put dough into oiled bowl, cover with a damp towel (sourdough likes a moist environment) and put somewhere to rise. (I usually heat up some water in the microwave to make that a damp warm environment and then put my dough in there with the door closed to rise). Let rise until dough has doubled in size. This will take 4-12 hours depending on how warm it is in your house. Punch down, form into whatever bread shapes you want to make and then let rise until doubled in size again. When it looks like it’s ready to bake preheat your oven to 400 degrees. Bake until done. It will be golden brown and sort of *thunk* when you tap at it. Probably 20-25 minutes depending on what bread shape you made.