In a medium sized saucepan, combine the sugar and the water. Stir just until combined.
Place the saucepan over medium heat. Let the sugar mixture cook, without stirring, until the sugar mixture turns a rich amber color. Take the mixture off the heat to stop the cooking process.
Add the butter to the saucepan and whisk to combine. Be very careful as the mixture is incredibly hot and will bubble up and steam when the butter is added.
Whisk in the heavy cream, followed by the vanilla and the salt until smooth.
Let the caramel cool in the pan for 10 minutes before transferring to a glass jar to cool completely.
Make the apple spice cupcakes
Heat the oven to 350F. Line a 12-cup muffin pan with cupcake liners.
In a medium bowl, whisk the flour, baking powder, baking soda, salt, cinnamon, nutmeg and cloves and whisk to combine. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, combine the butter, sugar and brown sugar. Beat on medium speed for 4-5 minutes until light and fluffy.
Add the eggs, one at a time, beating until they're fully mixed in. Scrape down the sides and up the bottom of the bowl with a rubber spatula after each addition. Beat in the vanilla extract.
Add the flour mixture into the mixer in three additions, alternating with the applesauce in two additions. Start and end with the flour. Mix until just combined.
Scrape down the sides and up the bottom of the bowl with a rubber spatula to ensure everything is fully mixed and incorporated.
Divide the batter into the liners. You will use every bit of this batter. Bake for 16-20 minutes, or until a toothpick inserted in the center comes out clean. Allow the cupcakes to cool completely before filling.
Make the caramel apple compote filling
While the cupcakes cool, make the apple compote. Combine the diced apples and lemon juice, and stir to combine.
In a skillet over medium-low heat, combine the butter and the caramel and cook until melted and bubbling. Whisk in the salt and cinnamon.
Add the apples to the caramel mixture. Cook until the apples have softened, and are a bit translucent, and the sauce has thickened, about 5-6 minutes. Allow the mixture to cool completely.
Make the brown butter cream cheese frosting
Place the butter in a light-colored skillet. Melt the butter over medium heat, stirring occasionally. Once melted, the butter will begin to foam. Keep stirring occasionally.
After 5-8 minutes, the butter will begin browning. There will be lightly browned specks forming at the bottom of the pan and it will have a nutty aroma.
Once browned to an amber color, remove from heat immediately and allow the butter to cool until solid, but still soft, like a thick paste.
In the bowl of a stand mixer fitted with the paddle attachment, combine the cooled brown butter, and the cream cheese. Mix until thoroughly combined.
Mix in the confectioner's sugar, a cup at a time, mixing after each addition until combined.
Add the salt and the vanilla.
Turn the mixer up to medium speed, and whip for 3 minutes. Scrape the bottom and sides of the bowl. Whip again for another 2 minutes.
Assemble the cupcakes
Using a sharp knife, cut a hole into the center of the cooled cupcakes to create a space for the apple filling. The piece you removed will be the shape of a cone.
Spoon the apple mixture inside each carved out cupcake. Fill the cupcake with apple filling to the top. Slice off the pointy end of the cone piece you removed so that it can fit on top of the filling. Place on top of the filling.
Use a large ice cream scoop to scoop heaping portions of the frosting onto each of the cupcakes.
Use a small, offset spatula to smooth out the frosting to the edges, while still maintaining the dome shape.
Place the peanuts in a shallow bowl. Roll the sides of the cupcakes through the peanuts.
Drizzle the salted caramel sauce over the cupcakes. Insert a popsicle stick or cake pop stick into the center, and serve.
These cupcakes can be stored in the refrigerator for 3 days. Serve at room temperature.