I can help since I've used them for both food and chop/drop. Most pigeon peas varieties are day length sensitive. In Florida that means they tend to grow vegetative during long days of summer and begin to flower as daylength shortens into fall and winter. They bear on branch tips so some formative pruning can increase the number of branch tips. The prunings can be used as chop/drop when they are vegetative then when fall approaches you can get the pea harvest.
After the peas finish near the end of the dry season you can get a massive chop/drop by pruning very low almost all the branches which will regrow during the rainy season. Depending on position, density and luck you might get 1-2 or 3 years before the pigeon peas reach old age and die off.
I agree with Peter there are other great long term perennial plants including legumes but in the very early stages of succession or just for a short cycle pigeon peas are easy and ideal dual purpose.
Here is a drone eye view of a first year pigeon pea hedge along both sides of a 100 ft long tree planting. There are 10 Sweet Tart mango trees in there, banana, plantain, papaya yam, cassava, sweet potato eggplant and many other plants, herbs, etc. The pigeon peas were direct seeded and thinned to one foot spacing. The pigeon peas lasted about 2 years and even after removing them a few volunteers still come up here and there into year 3-4. I did harvest many meals of fresh peas, froze some and eventually harvested 20 pounds dry peas. I considered it a success.
During the second year I planted banana between the tree beds @ 6 ft spacing and various longer term legume trees between each banana. The banana served to produce chop drop and by year 5 I expect the legume trees to be ready for chop/drop.
This pic shows them well grown just before a large chop/drop cycle.
I'm still using them elsewhere.
I see yours are planted in a grass lawn which does make mowing complicated. You could probably encircle a well mulched fruit tree in a hedge form and still mow around that. Just control them from growing inwards and crowding or shading the tree favoring the outward growing branches.