Preheat oven to 375°F (190°C). Line 2 baking sheets with parchment paper.
Using a permanent marker, draw 8 (2½-inch) circles 1 to 1½ inches apart on another sheet of parchment paper. Place paper with circles under parchment on a prepared pan. (The paper with circles is a template for piping.)
In a medium saucepan, bring butter, ½ cup (120 grams) water, milk, granulated sugar, and salt to a rolling boil over medium- high heat. Add flour, and stir with a wooden spoon until combined. Cook, stirring constantly, until a skin forms on bottom of pan and mixture pulls away from sides of pan and forms a ball, 1 to 2 minutes.
Transfer mixture to the bowl of a stand mixer fitted with the paddle attachment; beat at medium-low speed until dough cools slightly and is no longer steaming, 2 to 3 minutes. Add 4 eggs (200 grams), one at a time, beating until combined after each addition. (Batter will be shiny and will slowly move back together when a spatula is dragged through it; batter should also fall off paddle attachment so excess is left hanging in a “V” shape.) Add remaining 1 egg (50 grams) if necessary.
Transfer some of batter to a large pastry bag fitted with a ½-inch round piping tip (Ateco #806). Place piping tip in center of a drawn circle. Hold tip perpendicular ½ inch above pan and hold parchment paper steady, if necessary. Keeping tip steady, apply even pressure until batter reaches edges of drawn circle. Stop applying pressure, and move tip in a quick circular motion as you lift away. (You want to minimize points, but it’s OK if your dollops do have some peaks.) Repeat with remaining batter until pan is full. Dampen fingertip with water, and gently press down any points or ragged portions to create a smooth top, if necessary. Carefully slide template out from under piped batter, and place under parchment on remaining prepared pan. Repeat piping procedure with remaining batter.
Bake, one pan at a time, for 15 minutes. Rotate pan, and bake until fully puffed and golden brown, about 10 minutes more. Let cool completely on pan on a wire rack.
Clean bowl of stand mixer. Using the whisk attachment, beat cold cream and confectioners’ sugar at medium-high speed until soft peaks form. Add mascarpone and vanilla, and beat until stiff peaks form. Use immediately, or refrigerate until ready to use.
Cut cream puffs in half horizontally. Spread 3 to 4 tablespoons (25 to 34 grams) mascarpone whipped cream on bottom half of each puff. Top each with 2 tablespoons (40 grams) Apple Compote and top of puff. Top with Salted Caramel Sauce as desired. Serve immediately.