Set a large pan over medium-high heat and add olive oil. Add onions, jalapeno, and garlic, season with salt and pepper, and saute 5 minutes until translucent.
Add ground turkey and cook until done, breaking it up with a wooden spoon - about 7 to 10 minutes.
Add tomato paste and stir.
Add ketchup, gochujang, mustard, gochugaru flakes, fish sauce, brown sugar, tomato paste, and wine. Stir everything to combine.
Reduce heat and simmer for 10 to 12 minutes.
Finish with a splash of red wine vinegar.
Let stand 5 minutes to cool.
Add scoops of sloppy joe to hamburger buns, top with cheese if desired and serve.
Notes:
Feel free to use whatever ground meat that you want for these sloppy joes.