Preheat the oven to 325°F and lightly grease a 9-inch springform pan.
In a medium bowl, combine graham cracker crumbs, 1/4 cup sugar, salt, and melted butter, stirring until the crumbs are evenly moistened.
Press the crumb mixture firmly into the bottom of the prepared springform pan in an even layer.
Bake the crust for 10 minutes, then remove from the oven and let cool while you prepare the filling and raspberry swirl.
In a small saucepan, combine raspberries, 3 tablespoons sugar, and lemon juice over medium heat.
Cook, stirring and gently mashing, until the berries break down and the mixture thickens slightly, about 5 to 7 minutes.
Remove the raspberry mixture from the heat, press through a fine-mesh sieve if you prefer a smoother sauce, and let it cool to room temperature.
In a large mixing bowl, beat the softened cream cheese with 3/4 cup sugar on medium speed until smooth and silky, about 2 to 3 minutes, scraping down the bowl as needed.
Add the eggs one at a time on low speed, mixing just until each egg is incorporated and scraping the bowl between additions.
Add the sour cream and vanilla bean paste and mix on low speed until the batter is smooth and fully combined.
Pour the cheesecake filling over the cooled crust and smooth the top with a spatula.
Dollop spoonfuls of the cooled raspberry sauce over the surface of the filling.
Use a skewer or butter knife to gently swirl the raspberry sauce into the cheesecake batter, creating ribbons without overmixing.
Place the springform pan on a baking sheet to catch any drips, then bake at 325°F for 50 to 60 minutes, until the edges are set and the center still has a slight wobble.
Turn off the oven, crack the door open slightly, and let the cheesecake sit in the oven for 1 hour to cool gradually.
Remove the cheesecake from the oven and let it cool completely at room temperature.
Once cooled, cover the pan and refrigerate the cheesecake for at least 3 hours, or until fully chilled and set.
Run a thin knife around the edge of the pan before releasing the springform ring, slice, and serve chilled.