If you want to control when they hatch and have much control over how many, you need to use an incubator. You can’t control when or how often a hen goes broody no matter her breed. And hens have a limited capacity for the number of eggs they can cover. Eggs and hens come in different sizes. Some bantams can barely cover 4 regular sized-eggs. I’ve seen a full-sized hen cover and hatch 18 of her own eggs when she hid a nest. I’ve seen a full-sized hen have trouble covering 12 eggs the size she lays. To incubate successfully a hen needs to be able to comfortably cover all the eggs.
I prefer having a broody hatch the eggs and raise the chicks with the flock but I need about 40 to 45 chicks a year for my table. My flock is fairly small and my broodies can’t handle that. I use an incubator early in the spring for maybe 20 chicks and my broodies normally handle the rest later in the year.
There is a lot of debate on here about whether leaving eggs in the nest will cause a hen to go broody. I think this is part of your question. I’ve tried adding one golf ball a day or marking and adding a real egg a day to a nest until I got a dozen in there, then left them for a few weeks to see if a hen went broody. Nope, did not happen although my hens go broody. One time when I was gone on a trip the person that was taking care of the chickens was supposed to take all the eggs for herself. She did not do it. When I got back late one night the nests were full of eggs and a couple of hens were on them, acting kind of broody. I tossed the eggs the next day and both those hens quit acting broody and continued laying eggs. Maybe if I’d left them they would have kicked over into full broody mode. I’ll never know. One time I built up a bunch of eggs in one nest and a hen went broody, in a different nest.
I think if a hen is thinking about going broody having a nest full of eggs may help put her over the edge into full broody mode, but she has to be a hen that goes broody to start with and she has to be thinking about it. Many of us have had hens go broody on empty nests so having eggs in the nest is not a requirement for them to go broody.
Whether or not a hen goes broody depends on her genetics. Hens from production breeds tend to not go broody a lot. In a production flock a broody hen is not laying eggs but she is taking up space and costing money by eating until she starts laying again. It takes special handling to break her from being broody. Broodies are just generally permanently removed from the flock and incubators are used to hatch eggs. After a few generations of this you get a flock where the hens tend to not go broody. You can still get a broody hen from any breed, but some breeds are more likely to go broody than others. You can also get a hen from any breed that will never go broody.
All the eggs need to start incubation at the same time, whether in an incubator or under a broody, so they will hatch at the same time. Instead of leaving the eggs in the coop in the hopes that one will go broody, I suggest you collect the eggs every day so predators won’t find a treat in there if they visit at night (especially snakes). When a hen goes broody, start collecting the eggs you want her to hatch and give them all to her at the same time when you have enough. Even if you leave a bunch of eggs in the coop to try to entice one to go broody I suggest you collect fresh eggs for her to hatch and toss the old ones when you have enough to start her. Or cook the old eggs and feed them back to the flock.
Good luck with the adventure! Glad you joined us!