You asked about coring, but now you’re looking at all those slimy seeds. “Do I need to remove those too?” Relax. That’s a different problem.
Coring is for the stem and the tough white stuff. De-seeding is for making a less watery sauce or a perfect salsa. You can do both at once, but don’t stress.
If you really want to remove seeds after coring, just squeeze the tomato halves gently over the sink. The seeds and jelly will slide right out. It’s a little messy, but very satisfying.
