Using your stand mixer fitted with the dough hook, place the yeast and sugar into the bowl. Slowly pour in the warm water and stir together gently just a few times. Let sit until the yeast has doubled and is puffed and foamy on top, for about 8 to 10 minutes.
Add in the melted butter, warm eggnog, mascarpone and egg, and stir to combine. Add in the flour, salt and vanilla. Using your stand mixer again, knead the dough with the dough hook until the dough is smooth and forms a ball, for about 5 minutes. I start out using a low setting on my stand mixer and then go to just a slightly faster setting for just a little as the dough beings to form a ball. The dough may be sticky but that's ok.
Remove the dough from the bowl and place onto a lightly floured work surface. Use a little flour if the dough is really sticky to help you shape into a ball and place into a large greased bowl and cover with plastic wrap, and then with a kitchen towel (or two). Let the dough rise in a warm area for about 1 hour or until doubled in size. I like to leave my bowl next to my oven.