To make the dough: In a small saucepan (or using the microwave), heat milk and butter until melted and lukewarm to the touch (110F-115F, no more).
Place flour, sugar, and yeast in the bowl of a standing mixer and mix to combine, then stir in salt. Add egg and milk-butter mixture. Attach dough hook and mix on low speed for 3 minutes, until dough starts to come together. If dough is too sticky and looks more like batter than dough, add a bit more flour, 2 tablespoons at a time (but don’t be tempted to add a lot, the dough should be rather soft). Increase mixer speed to medium-low and mix for another 10 minutes, until dough pulls away from the sides of the bowl (it’s ok if it sticks to the bottom). Stop periodically to scrape down the sides and bottom of the bowl. Cover dough with plastic wrap and let rest in a warm place for 1.5-2 hours, until doubled in size. Alternatively, you can refrigerate the dough overnight; it will rise slowly and be ready for the next step by morning.
Meanwhile, make the apple filling: In a medium bowl, toss together apples and lemon juice. In another bowl, mix together sugar, flour, salt, and cinnamon, then add it to the apples and toss to combine. Add vanilla, and mix again.
In a large heavy skillet over medium heat, melt butter. Add apple mixture and cook, stirring occasionally, until the apples are tender but not mushy and coated with a caramel-like sauce, about 8 minutes. Stir in raisins and remove from heat. Transfer to a large bowl and let cool to room temperature, about 30 minutes (or, you can prepare it a day before and keep it in the fridge).
Keep preparing the dough: When dough has doubled in size, gently punch it to remove air. Roll dough into an 18x10 inch (45x25 cm) rectangle. Spread apple filling evenly, leaving a small border around the edges of the long sides of the rectangle. Starting with the long edge, roll dough to form a log, and pinch to seal the seam.
Cut into 12 equal size pieces and place cut side up on a greased 9x13-inch pan. Cover and let rest to rise for about 1-1¼ hours, until dough has almost filled the pan.
Meanwhile, preheat oven to 350F/175C.
Bake rolls in the preheated oven for 25-30 minutes, until the tops have browned and a skewer inserted into the rolls comes out clean. If the rolls brown quickly while baking, cover them loosely with aluminum foil. Allow rolls to cool completely on a wire rack
Serve warm or at room temperature.
Rolls are best the same day they’re made. You can freeze any leftovers and rewarm them when ready to eat.