In a small bowl whisk the instant yeast with the lukewarm milk so it dissolves.
Add the flour and salt to the bowl of your stand mixer fitted with the dough hook. Add the yeast mixture, butter and honey. Start mixing on low speed and gradually add the eggs. Scrape down the sides of the bowl, then turn up the speed to high and continue mixing for 10 to 15 minutes to develop the gluten. The dough should be a smooth elastic dough.
Transfer the dough to a clean bowl, use a bench scraper to help transfer the dough. Cover the bowl with plastic wrap and allow it to proof, in a draft free environment, for 30 minutes.
Generously butter a rum baba mold pan, or a muffin pan, then lightly dust each mold with flour, shaking off any excess. Wipe the top with the mold with a clean towel or paper towels to remove any excess flour.
Using 2 tablespoons, transfer dough into each mold, halfway through. Place the mold pan in a warm draft free environment and allow it to proof for another 1 to 2 hours, until doubled in size.
Preheat the oven to 375°F.
Place the mold pan in the oven and bake for 11 to 13 minutes or until golden brown on top. To check if they're done, insert a toothpick in the center of a baba, and it should come out clean when they're done.
Carefully remove the babas to a cooling rack immediately and allow to come to room temperature.