Dimming 1w leds with transistor and walwart issues

OK, next thing to learn is that LEDs don't work well if you try to control their voltage, they work much better if you control their current. If your LEDs need 350mA then you need a special "constant current" circuit that allows that many amps to pass.

The reason is that LEDs don't have a constant resistance, their resistance varies with voltage. Even tiny errors in voltage can lead to big errors in current, enough to damage the LED. Every LED is slightly different and needs a slightly different voltage so the only way to avoid those errors is to control the current.

You can get a special "led driver" for this or look for examples in these forums.