Prepare the souffle: Preheat the oven to 375 degrees F and generously butter a 4-cup souffle dish. Wrap the dish with a buttered parchment collar (see right). Sprinkle the inside with sugar and shake out the excess.
Combine the cream cheese, goat cheese, orange and lemon zests and the vanilla in a large bowl. Beat with a mixer on medium-high speed until smooth and fluffy, about 2 minutes. Beat in the egg yolks until incorporated. (At this point, the mixture can be covered and refrigerated up to 6 hours; bring to room temperature before continuing.)
When ready to bake, put the egg whites in a large bowl and beat with a mixer on medium speed until foamy. (Make sure the bowl and beaters are clean.) Increase the speed to medium high and gradually add 6 tablespoons sugar; beat until stiff and glossy.
Stir one-third of the egg whites into the cheese mixture to lighten it, then gently fold in the rest until just incorporated. (It's OK if a few streaks of egg white remain.) Transfer the mixture to the prepared dish and bake in the center of the oven until puffed and golden, about 35 minutes.
Meanwhile, make the compote: Combine the orange juice, honey and a pinch of salt in a small saucepan over medium heat and simmer until slightly thickened, about 4 minutes. Let cool slightly, then add the orange segments. Remove the souffle from the oven and remove the parchment collar. Serve immediately with the compote-the souffle will start sinking after a couple of minutes.