This is an interesting topic. I can't do a thorough search at this time but these are what I gathered in the time I have this morning - starting points at best; possible not worth much. Please share when you find interesting pieces.
This is not behind a pay wall
https://ejfood.org/index.php/ejfood/article/view/456
"...Despite the indigenous chicken's many natural advantages, broodiness continues to be a substantial barrier to minimizing egg production and economic losses. Prolactin is the primary regulator of broodiness. ..."
This is partially avialible (more than abstract)
I like it because the associated studies are more helpful than most. Eh, these are also mostly behind pay walls but I think they give a rich field to mine more search terms. I would sort through them to make a list of the most promising to read at a college library. Although it has been several years since I did that as a non-student. Even then, some colleges were beginning to have more restrictions on that (either limiting numbers or time or visits), I don't know how much that has spread.
https://www.sciencedirect.com/science/article/abs/pii/S0016648009001373
"...In this review we emphasize the potential ability of prolactin to mediate parental investment in birds (i.e., the trade-off between survival and parental effort). We review (1) the neurobehavioral interactions that link avian parental behavior and prolactin secretion, (2) the effects of stressors (acute and chronic) and energetic constraints on prolactin levels during the parental phase and (3) the modulation of circulating prolactin levels by acute stressors. ...Finally, we emphasize the importance of considering possible interactions between corticosterone and prolactin in the regulation of parental investment in birds..."
This one is behind a pay wall, it is here for terms to search for
https://onlinelibrary.wiley.com/doi/abs/10.1002/jcp.26844
The postovulatory follicle (POF) in birds is an enigmatic structure, the function of which remains largely unknown. Previous studies on chickens have shown that removal of POFs leads to the postponement of oviposition and the disturbance of broody behavior.
I didn't find much on POF and broodiness but found this about pausing for molt interesting.. it is from
https://www.mdpi.com/1422-0067/22/15/8056
"An important phenomenon in the reproductive cycle of female birds is the regression of reproductive organs and the subsequent pause in laying and molting at the end of the reproductive season or after about a year of egg laying. This event leads to rejuvenation of reproductive tissues by the removal of old cells and proliferation and differentiation of new cells. During this period, yellow hierarchical follicles in the ovary undergo atresia. "