Add the eggs to the yeast mixture & beat until well combined. Add 2 1/2 cups of flour & salt. Mix for 4 minutes on medium setting, scraping the dough down a few times.
Add the butter, 2 tablespoons at a time. (It’s important the butter is soft or it won’t incorporate thoroughly.) Continue kneading with the dough hook, scraping the bowl down a few times, for about 5 minutes until the dough is smooth & shiny. If dough is too sticky, add a little more of the remaining 1/2 cup of flour, a couple of tablespoons at a time. Grease a large, clean bowl. Scrape the dough onto a lightly floured, smooth surface & knead until smooth. Shape the dough into a round & place into the greased bowl. Cover the bowl with plastic wrap & let rise in a warm place for 2 hours
Punch the dough down lightly & fold it over itself four or five times, leaving the dough in the bowl. Shape into a round, cover the bowl with plastic wrap & let rise in a warm place for 45 minutes.
Line a 12-hole muffin pan with tulip muffin liners (it’s important to use the tall pointy liners as shown in the photographs). Link in post.
Combine the apple & the brown sugar mixture until thoroughly mixed.
Shape the dough into 12 balls of equal size on a lightly floured surface (I use a scale for this – weigh the dough & divide by 12. It’s usually 3 oz, approximately, per ball).
Roll out a ball onto a lightly floured surface until 3 1/2 x 5 inch rectangle with a short side towards you. Spread about 2 heaping tablespoons of apple mixture over dough, leaving a 1/2-inch border at the top. Roll up firmly from the short end closest to you to form a log. Cut each log into 5 equal pieces & place into a muffin liner in a haphazard way. Repeat with remaining dough balls & filling.