I’d like to turn on a 1 watt LED from my Photon. I’m looking at something like this which takes 3-3.4v and 350mA: https://www.amazon.com/6000K-6500K-300mA-350mA-Intensity-Components-Lighting/dp/B01DBZHR1U
I’ve looked at some 3.3v relays but they’re pretty bulky: https://www.amazon.com/3V-Relay-Module-Optocoupler-Development/dp/B01M0E6SQM
Shouldn’t I be able to do this with a simple MOSFET? Ideally I’d have the same power supply going to my Photon (Lipo battery) switched on through the transistor and to the LED.
If I’m not crazy, any recommendations on transistor part numbers? Maybe even just a 2N2222?
1W at 3.3V is approx. 303mA. I think any MOSFET with at least a 350mA (better to chose 500ma or so for a safety factor) current rating would work. Would this work for your needs? It is an N-Channel MOSFET rated at 500mA (derated to 350mA at 85°C):
Perhaps! Any idea if it comes in through-hole package?
Also, the LED is rated for 3.0v-3.4v, but a fully charged lipo battery is around 4.2v. What can I put between the two so that voltage is brought down to ~3.4v when the battery is full, but not below 3.0v when the battery is lower? Hmm…
Then you probably don't want a discrete MOSFET but rather a constant-current LED driver. An LED-driver would drive a constant current through the LED irregardless of voltage applied. You could create some kind of current mirror with discrete transistors but that EE class I didn't do so well in. I would rather search digikey for the component that suits my needs rather than re-create the wheel.
Hmm, I see a bunch of those on Mouser but they’re HUGE: https://www.mouser.com/Optoelectronics/LED-Lighting/LED-Lighting-Electronics/LED-Drivers-Power-Supplies/_/N-b1asl?P=1yzot00 I was hoping to get something nice and compact.
Maybe this LED will a future “enhancement” to my project. 
I said an LED driver, not an LED power supply. Here are some driver chips on Mouser:
https://www.mouser.com/Optoelectronics/Drivers/LED-Lighting-Drivers/_/N-7zi53Z1yzvvqxZgjdhub?Rl=7zi53ZerbbZ1z0w877Z1z0w9csSGT&Ns=Pricing|0
But none in a through-hole package. Everything you need is in SMD packages.
Or on digikey as I find their site a bit easier to navigate for certain components.
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Hmm…tried tweaking the filters but can’t seem to find one in the range I need. If I get one with 300-400mA then it needs like 50v. If I find out with 3v+ input then it’s only outputting like 5mA. Ugh.
On that digikey link, it was already filtered down to give you LED Drivers with at least 400mA current. It was fairly easy to apply another filter for “output voltage”. This looks like it does what you want and in a package that you might be able to solder by hand:
Don’t be surprised but there are numerous passives needed in the application circuit.
If you looking for a through hole part with low components you could use a LM317 set up for current mode operation.