Depending on the vegetable plant, some legginess can be corrected during transplant. Plants in the tomato family, including peppers and eggplant, produce new roots from their lower stem if it is buried. This is called trenching.  When you transplant them outside, bury the stems as shown in the attached picture. Many species of plants can't tolerate that treatment and their leggy stems will just rot if buried. Be sure you harden off the seedlings by taking them out of doors for an hour the first day at the warmest part of the day, and then gradually working up to a full day over a week, weather depending. Also, make sure the soil is warm before planting. These seedlings are more fragile because of the stretching and need to be pampered.