In a medium bowl, combine 1 tablespoon of the yeast with 3/4 cup of the warm milk and stir to dissolve the yeast. Add 3/4 cup of the flour and stir to create a smooth paste. Cover the bowl with plastic wrap and let the flour mixture rest in a warm place for 30 minutes.
Once 30 minutes have passed, in the bowl of a stand mixer fitted with the paddle attachment, combine the remaining 1 tablespoon plus 1 teaspoon of yeast with the remaining 1/4 cup milk. Add the rested flour mixture along with the vanilla and egg yolks and mix on low until the ingredients are incorporated and the dough is smooth, about 30 seconds. Turn off the mixer and add 1 cup of flour, along with the sugar and salt. Mix on medium until the dough starts to come together, about 30 seconds. Add the butter and mix on medium until it's incorporated, about another 30 seconds.
Remove the paddle attachment from the mixer, and switch to the dough hook. Start adding the remaining flour, 1/4 cup at a time and knead the dough on medium until it completely pulls away from the side of the bowl and is smooth and not too sticky, about 1 minute. The dough will be very soft and moist but not so sticky that you can't roll it out. Cover the bowl with plastic wrap and let the dough rest in a warm place for 1 hour. After one hour, gently press down on the dough to remove any gas bubbles. At this point you can either roll the dough out or chill the dough, covered, for up to 24 hours.
When ready to roll out the dough, line 2 baking sheets with parchment. Lightly flour a work surface and roll out the dough to a 1/2-inch thickness. Using doughnut or cookie cutters, cut out 1 1/2-inch-diameter rounds. Arrange the doughnuts on the prepared baking sheet, leaving at least 1 inch between doughnuts. Cover the doughnuts loosely with plastic wrap and let them proof in a warm place, about 20-30 minutes.
Meanwhile make the caramel, in a large heavy bottomed pot, heat the sugar over medium high heat. As the sugar begins to melt, stir it frequently to help it melt evenly. Continue to cook and stir until the caramel begins to turn a light amber color. Remove from heat and let sit 2 minutes. Then carefully stir in the butter. Now slowly stir in the heavy cream and salt (it will bubble up quite a bit). Whisk to incorporate. Some of the sugar will harden around the spoon or whisk, this is fine. Return the pot to medium heat and simmer 3-4 minutes or until the sugar has melted and the sauce is smooth. Remove from the heat, stir in the bourbon and chocolate.
To make the cheesecake filling, add the cream cheese, heavy cream, sugar, vanilla and peanut butter to the bowl of a stand mixer (or a medium mixing bowl). Beat on medium speed until light and fluffy, about 5 minutes. Spoon the cheesecake filling into a pastry bag fitted with a tip or just a ziplock bag with the corner snipped off.
In a heavy-bottomed large pot or deep fryer, heat at least 2 inches of oil until a deep-fry thermometer registers 350 degrees F. Working in batches, use a slotted metal spoon or spatula to carefully place the doughnuts in the hot oil. Fry, flipping once, until light golden brown, 1 to 2 minutes per side. When done, transfer a the wire rack. Make sure to return the oil to 350 degrees F. between batches. Let the doughnuts cool slightly (about 2-5 minutes) before filling.
Pierce base of each doughnut with piping tube and pipe a little cheesecake filling into each. Serve warm with the warmed salted chocolate caramel. Grab cold milk. Enjoy!