Place your cream cheese and sugar into a large mixing bowl, and using an electric hand mixer, mix on high until the cream cheese and sugar have become completely smooth. Try to smooth out any lumps in the mixture before proceeding.
Once the sugar and cream cheese are combined, add the sour cream, vanilla, and one egg. Mix until combined.
Add the last 2 eggs one at a time, mixing between each addition until the cheesecake batter is smooth with no lumps remaining.
Once smooth, stir in the Key Lime juice and vanilla bean paste until well mixed.
Pour the cheesecake mix into the crust inside the springform pan, and smooth out the top.
Place the cheesecake into the oven and bake for 10 minutes at 425 degrees F.
Once the 10 minutes have passed, open the oven door to allow some heat to escape, close it again, and decrease the oven temperature to 325 degrees F. Continue baking for another 40-50 minutes until the sides have set, but the center still has a little bit of a wobble to it.
Once done, pull from the oven, and allow to cool to room temperature before placing in the fridge to finish setting. This will help the cheesecake avoid cracking. Allow to set for 2-4 hours in the fridge.
Once the cheesecake has set, whip together the heavy cream and sugar to make homemade whipped cream. Remove the cheesecake from the fridge and top it with your whipped cream and lime slices. Slice, serve, and enjoy!