I would wait until they outgrow the root space in their current container or at least until the plants are about 2 inches high or more. Transplanting is rough on seedlings, and the ones you're describing are still very tender. I have started sowing in larger peat pots so no transplant is needed. This way they grow up in the same environment until they're planted in the garden. Hope this helps.

I respectfully have to disagree with the info next-generation provided. First because you never want young seedlings to get root bound, second because staged-transplanting is a normal and important part of the growing from seed process (many discussions here about this), and third because seed starting in peat pots is very problematic, especially large peat pots. Again, many discussions here about this.

Your broccoli seedlings may not be salvageable so I would recommend starting more while trying to salvage these. The existing seedlings need to be carefully untangled and transplanted now, individually into another container with a good growing mix, and transplanted deeply. Bury all of the stem and all of the growth upto just below the very top 2 leaves.

Water well - do not feed right now - and set them out of the hot sun in a cool location (60-65 degrees) for several days. When you see new growth they can be moved back under the lights. I hope you are supplying supplemental lighting? Normally takes 2-3 days for new growth to develop.

The same holds for the eggplant and they have a much better chance of recovering than the broccoli does.

Hope this helps and next time - cover off and off the heat and under the lights just as soon as the break the surface of the soil.

Dave

i made the same mistake with my peppers this year and lost all my hot peppers I plan on restarting them tommorrow I thought that I was supposed to leave them on the heat untill the true leaves not when they broke the soil