The Cube Rule is the most definitive and authoritative categorization of food topology I have encountered. I refer to it often in food related arguments.
Although the bagel half on the bottom and the top are split toroids, topologically they are flat (you can 'deform' it into a flat plane if you squish it). This is assuming it hasn't been cut down the center as well.
The filling of PB&J is between the two starches. Therefore this is Food Type 2: Sandwich.
Ah I see. This looks a bit different than OP's image. This requires further research in food cube science.
I do believe this configuration that you listed could be a new sub-Type of food topology. It combines four starches with filling in between, as two Type II sandwiches orthogonally configured.
Since you can theoretically make modifications like this to the other Types, it might be easier to make these new configurations subtypes of the main categories instead of making a Type VII (we should reserve these for 4D foods).
This particular case is a biaxial Type IIa sandwich.
I suppose it is neither a taco or a sand which, however it lives within the sandwich family. What's weird is if we take the inner radius as it runs towards zero it would look no different to a sandwich (save the weirdly thick bread that looks similar to a burger), but it would be topologically different shape.
I suppose it depends on if you consider a bagle split more naturally a sandwich or not, and, if so, then it matters if the if the space of the filling being connected matters or not.