Preheat oven to 400˚F.
Bring a medium pot of water to a boil, then remove from heat. Add the shallots to the pot (whole and unpeeled), cover, and let sit for 6-7 minutes.
Drain the shallots. When they are cool enough to handle, Slice off both ends, then remove the peel (it should come off easily!). Slice each shallot into ½-inch thick rounds. Set aside.
Roll out the puff pastry on a lightly floured surface until it's large enough that you can cut out an 11-inch round. Return to the refrigerator while you make the caramel.
Heat a 10-inch stainless steel skillet over medium and add in the sugar and water. Gently stir just until the sugar is dissolved, then let it boil untouched for 4-5 minutes, until it's golden brown.
Carefully add in the butter, balsamic, rosemary, salt and pepper (the mixture will bubble up a little bit) and whisk well. Let it simmer for 30-60 seconds while whisking. Remove from heat.
Arrange the shallots atop the balsamic caramel, placing them as close together as possible.
Place the puff pastry over the top and gently tuck in the edges.
Bake for 30 minutes until the puff pastry is golden brown, then cover the puff pastry with aluminum foil and return to the oven for another 30-35 minutes.
Remove from the oven and let sit for 5-10 minutes. Carefully tilt the pan and check to see if it looks like the caramel is watery. If so, turn on a burner to medium-high and let it simmer for 2-3 minutes until it starts to thicken again. (This can happen depending on how much moisture your shallots have.)
Let it cool for 15-20 minutes, then carefully flip onto a large plate or cutting board. Top with crumbled goat cheese before slicing. Enjoy!
