Preheat the oven to 350°F. Grease and flour a 10- to 12-cup Bundt pan, getting into every crevice.
In a large bowl, whisk together the flour, sugar, baking soda, cocoa and salt.
In another bowl, whisk the eggs, oil, buttermilk, vanilla, food coloring and vinegar until smooth.
Pour the wet ingredients into the dry and stir until just combined.
For the filling, beat the cream cheese, sugar, egg and vanilla until smooth.
Pour about two-thirds of the cake batter into the pan. Spoon the cream cheese filling in a ring over the batter, keeping it away from the sides of the pan. Top with the remaining batter.
Bake for 50–60 minutes, until a tester inserted into the cake near the outer edge comes out clean.
Cool in the pan for 15 minutes, then turn out onto a rack. Cool completely before slicing.