Preheat the oven to 180°C. Wrap the exterior of a 9-inch spring-form tin tightly in three layers of tin foil, ensuring there are no rips or crevices for water to sneak through; set aside.
First, the crust. In a large bowl, mix together all of the crust ingredients. Using your fingers (or the base of a measuring cup), press the mixture firmly into bottom & up the sides of your prepared tin. Bake the crust until set, about 10-minutes. Leave to cool on a wire rack & reduce the oven temp to 160°C.
Next, make the berry swirl. In a food processor, whiz together the raspberries & the sugar until smooth, about 30 seconds. Pour the puree through a fine sieve into a small bowl; set aside. Discard the solids.
Now, the cheesecake. In a large bowl, use an electric whisk to beat the cream cheese until fluffy, about 3-minutes. With mixer on low, add the sugar in a steady stream, scraping down the edges of the bowl as you go. Add the vanilla extract & mix thoroughly. Add eggs one at a time, mixing each until just combined & scraping down the bowl.
Pour the filling over the par-baked crust. Use a piping bag (or something similar) to dot the raspberry sauce over the top of the filling & use a skewer to swirl the sauce decoratively through the filling. (If you have any spare sauce, keep it to garnish the finished cheesecake with!)
Place the uncooked cheesecake inside a large roasting tin. Carefully pour boiling water into roasting tin until it reaches halfway up the sides of the cheesecake tin. Very carefully transfer the whole thing to the preheated oven. Bake until the cheesecake is still slightly wobbly in the center, but is mostly set, 65-70 minutes. (A toothpick inserted near the center should not have wet, thin batter on it when removed.)
Once cooked, transfer the cheesecake to a wire rack, remove the tin foil, & leave it to cool entirely to room temperature. When cooled completely, refrigerate the cheesecake – uncovered – for at least 6 hours, preferably overnight.
Before cutting the cheesecake, run a knife around the edges of the tin & gently unmold it. Serve the cheesecake in generous wedges, topped with the leftover raspberry puree.