Make the dough- Mix the flour, yeast, sugar, and salt. Pour in the milk and melted butter. Stir to combine. Add in the egg and yolk and continue to stir. Pour on to the counter and knead for about 7 minutes until smooth to the touch. (you could also do this in a stand mixer) Put into a greased bowl covered with plastic wrap and allow to rise for 2 hours or until at least doubled in size.
Roll out the dough to about a half inch thin and cut out donut rounds. Place on a floured surface and brush with melted butter. Cover and allow to rise about an hour.
Bring oil to 350 and fry the donuts in batches, about 1 or 2 minutes per side. Remove from oil to a paper towel or drying rack.
Use a knife to make a cut about half way through the donuts, opening them up for stuffing
Mix the lobster meat with the melted butter and stir to combine. Warm this mixture up in a frying pan if needed. Season with salt to taste. Stuff the meat into the donuts.
Mix the mayo, lemon juice, and garlic in a bowl. Season with salt. Drizzle this mixture over the stuffed donuts. Top with chive and chili flake.