i find foliar feeding to be helpful in young growth development of basils. Try using a fish emulsion, seaweed, or kelp based organic fertilizer & dilute with water.
the back of the bottle or bag/box should give you directions on how to use, if not, use maybe 1TBSP to a gallon the most, and foliar spray with that
homedepot or lowes usually carries a safer product that is fish or seaweed based or you can be sure to find one at a nursery/ garden store.
also compost as a top dress will help speed things up a bit and you can always amend the soil, the next time you plan on transplanting.