Controlling full 12V of brightness out of LED strip (WEMOS D1 mini or other)

I'm working on a project to control some 12V analog-LED light strips. My understanding of electronics is very limited, but I'm learning.

MY QUESTION: What is the best way to completely control the full range of 12V LEDS using an ardunio device? The projects I've found online work to vary lights in all sorts of ways, but not at full brightness. What I have done is below, but I'm really looking for the best way to do this.

EXAMPLE SETUP: I followed the basic plan from this link: Jerome Bernard: RGB Led Strip controlled by an Arduino

This gist of this is as I understand it: 12V connects to the LED strip and then the WEMOS (powered from USB) controls the RGB levels by varying the gate voltage of N-channel MOSFETS, which affects the strip.

WHAT HAPPENS: Even when the WEMOS D1 analog pins for the RGB wires are set to 255, the voltage of the lights is are about 9V, not 12V. So, the lights are not as bright as they can be.

I can find various links which explain MOSFET things about the gate voltage, etc., but nothing about how to actually make a system that works just like those super cheap LED Remote Control Power Supply boxes with accompanying remotes do.

SIMPLER QUESTION: Should I just put 15V into the lights? If so, something tells me the AnalogWrite values are not going to be linear with respect to the voltage passed around the LED light circuit.

Thanks for any direction on this, it seems like an issue no one directly has addressed.

mobial:
Even when the WEMOS D1 analog pins for the RGB wires are set to 255, the voltage of the lights is are about 9V, not 12V.

It is possible that the power supply is unable to provide the required current and the voltage is therefore dropping. Try measuring the PSU output voltage when the LEDs are full-on and when they are at lower brightness and see if that is a possible cause.

Which mosfets are you using.
An IRFZ44N, as linked to in the article, is not a logic level mosfet.
It won't fully turn on with 5volt logic, and is totally unsuitable for the 3.3volt logic of a Wemos.
Leo..

The mosfets I am using are IRLB8721.

mobial:
The mosfets I am using are IRLB8721.

The datasheet shows that this mosfet can only switch a couple of amps with 3volt gate drive.
So what is your LED strip using.
Leo..