Powdery mildew. Yeah, neem is what i'd use. Use it in the evening so the hot Sun doesn't hit leaves fresh sprayed. Water them well, then spray.

Could be powdery mildew....starts as whites spots on the underside of leaves but eventually covers the entire leaf with powdery areas....

There is a possibility that you can control it with a baking soda spray applied once a week:
1 teaspoon baking soda to 1 quart water.
Note though that if you can't control it it will spread to other plants.

The most common solution is to thin your plants, remove and destroy all infected parts, disinfect your hands and tools in a bleach solution: 1 part bleach 4 parts water after each cut.

In addition to pruning: apply a cooper based fungicide every 7 to 10 days (stop 3 to 4 weeks before harvest).

As for NEEM it is used on insects and works as a repellent and insecticide.