Grease a 9-inch wide and at least 2 and 1/2-inch deep springform cake pan and line the bottom with parchment paper. Cut the parchment paper into strips as wide as the depth of your springform pan and line the sides with them, as well. Set aside.

For the crust, mix together the graham cracker crumbs, sugar, butter, and salt in a medium bowl until sand-like in texture. Empty the crust mixture into the bottom of the springform pan and press it into an even layer at the bottom. Set aside.

If you want to, you can make the strawberry balsamic compote ahead of time and refrigerate overnight. For the compote, mix the chopped strawberries, sugar, balsamic vinegar, and black pepper together in a small saucepan. Bring to a boil over medium heat, then reduce heat to low and simmer for 20 to 25 minutes, until the strawberries have softened and released some of their juices, stirring every 5 minutes. Remove from heat and allow the mixture to cool to room temperature. If making ahead of time, store in an airtight container in the refrigerator until use, and allow it to come to room temperature before incorporating it into the cheesecake.

In the bowl of an electric mixer fitted with the paddle attachment, mix together the cream cheese and sugar at medium speed until combined. Add the creme fraiche or sour cream in 4 increments, waiting until incorporated and smooth before adding the next one. Beat until smooth and fluffy, about 3 minutes. Reduce speed to medium low and add the eggs, one at a time, making sure each egg is completely incorporated and scraping down the sides of the bowl before adding the next egg. Add the vanilla and 1/3 of the strawberry balsamic compote to the cheesecake mixture and stir to incorporate.

Preheat the oven to 325 degrees Fahrenheit. Fill a casserole dish 2 inches deep with water and place on the bottom rack of the oven. Position another rack in the center of the oven.

Place the springform pan onto a lipped baking sheet. Pour the cheesecake mixture into the springform pan and add HALF of the remaining strawberry compote to the pan, one spoonful at a time to make little red spots on the cheesecake's surface. Run a butter knife through the surface of the cheesecake to make some fun little swirls. Place the baking sheet in the oven. Bake until the top of the cheesecake is golden brown and the cheesecake is still slightly jiggly but set, about 1 hour and 20 to 1 hour and 30 minutes.

Turn the oven off and leave the door ajar to allow it to gradually cool to room temperature over a couple hours, then remove the springform pan from the casserole pan and place the springform pan in the refrigerator for at least 4 hours. Remove it from the refrigerator and remove the sides of the springform pan and the side pieces of parchment paper. Spread the remaining strawberry compote over the cheesecake and top with the desired amount of fresh strawberries. Serve immediately.