Heat the olive oil in a large skillet or Dutch oven over medium heat.
Add the chopped onion, cover the skillet, and cook for about 5 minutes, or until the onion has softened and become translucent.
Stir in the frozen veggie burger crumbles and the drained diced green chiles, breaking up any large clumps with a spoon.
Pour in the ketchup, yellow mustard, and sweet pickle relish.
Stir everything together until well combined.
Season generously with salt and freshly ground black pepper to your liking.
Bring the mixture to a gentle simmer and cook, stirring occasionally, for about 10 minutes to allow the flavors to meld and the mixture to heat through completely.
To serve, spoon the hot sloppy joe mixture generously onto each sandwich bun and serve immediately.