It depends upon your area, which I'm not familiar with.
Here, yes, we can start broccoli in August, though we have to be careful. It's a balancing act, depending upon the year. Some are hotter than others, and some years it's hot for a longer period of time. I've had to replant when it was too early because of a longer than usual hot season.
We can plant green peas in the fall/end of summer, my preference, and/or in the spring, as soon as the ground can be worked.
The best way to approach fall planting is to get your first expected frost date and count backwards using the crops latest maturity date and then add 2-3 weeks to that. For instance, if you want to plant an spinach that mature in about 30-35 days and your first frost is mid-October (we'll use Oct. 15) you would count back 35 days and add 2 weeks to that. So this gives you a planting date around the first week of September.
The crops that take the longest to mature are cauliflower and cabbages about 70-75 days. Most cool season crops can take a light frost if one comes a little earlier than expected.
Another thing to consider is the ever shortening daylight. In the fall I can grow only the fast growing varieties of cool season crops, and they generally have to be under 50 days because, even though it's not that cold yet here in New England, there just isn't enough daylight by the end of October to bring things to a good harvest size in time.