Do recessed light fixtures with local switches exist?
To solve the problem of having only one switch per room but need for more lights, I went for a smart lighting system. By now there's plenty of systems available that you can compare and choose from, but based on my own experience, I can recommend Philips Hue system because it's well supported, it has lively user communities that you can easily get help from when you need assistance, they have quite a bit of different kinds of lamps (and now even other smart devices and products from other brands) that can be integrated to the system, and for LEDs (that can notoriously produce ugly dull light), the white light is good enough quality because the bulbs now use a slightly different method to produce it than what you might typically see. 
Philips will seem expensive once you start out (I considered for about two years), but once you have it, I've personally felt that it does pay off because it's so flexible and can solve problems such as this.
Currently Philips Hue seems to have a few recessed lights that belong to the "White Ambiance" range, meaning that they are dimmable, and you can adjust their color temperature from a very cold bluish daylight, to white, to warm light that all the way resembles the color temperature of a candle. Your eyes really appreciate that in the late evenings.

Now, how individually?
The Hue App (or third party computer programs) will allow you to adjust single light bulbs individually if you need that kind of precision. But if you actually meant that you want to control this big bunch of lights as several sub-groups instead of all at once, you can use the app to specify which bulbs belong to which group. Then, at the time of writing this, Philips has two physical accessories that you can use just like wall switches: Hue Remote, or Hue Tap. They can be attached to a wall like a switch, or they can go with you like a remote control. I personally find Hue Remote a better product. The official Hue app allows you to program what the remote control does, so you can choose to give commands to all lights or just some of those groups that you created. There's several third party apps that will allow you to program even more actions to a single remote controller than is officially possible. For example, iConnectHue which is for iOS, is one of those. The Hue Remote has four buttons, but with a third party app, you can program extra actions to it so the buttons have more in them if you press it vs. hold it, or press it once vs. press it four times. This of course means that you'd have to remember what you've programmed as the extra actions, but it's one way to avoid having to buy multiple Hue Remotes if you're not up for it.
For the lights to work correctly, you leave the electrical original switch ON at all times, and only use the remotes or the app or other ways to command the lights to go off when you want. The lights will be switched off, but because the electricity in them is still on, they will be ready to receive the next remote command that switches them on again, be it one of them, some of them or all of them.

There are other brands, but I don't have personal experiences to share about their quality. There are people who make Youtube videos or blogs about comparing and reviewing products, but unless you know the person's agenda, it's possible that they're being paid money to endorse products, so you can't get an objective and realistic review. If everything seems too perfect and flawless, it might be a paid endorsement.
If you were to think of adopting a smart light system, do consider the future of the manufacturer of it: If you buy a cheap lamp from a firm that no one's ever heard of and you can't find a manufacturer's website with any signs of support and professionalism in sight, the chances are that it is just a really cheap go at competing at the market of smart lighting, and when you encounter problems or the lamp malfunctions far too soon, you don't have any support, guarantees or community help available. This is not to say that Philips would be the only viable option, there are others, but I'd advise not to go for the cheap anonymous replicas that you'd quite probably end up regretting.