The first thing that you have to do is to build it in your mind. It is hard but that's how the questions about building it will arise.
Lets take for example your soldering idea.
1. You need power
2. You have to read the temperature
3. You have to control the power according to temperature
4. You need some way to interface with the user.
Now lets start building each part.
1: How to calculate how much power do I need? (Depends on heating element and control circuit)
What voltage do I need? (one value depends on heating element and the others to control circuit)
2. Does your iron have integrated sensor?
If yes what type? PTC, NTC, Thermocouple?
According to this you know what circuit you will need to transform sensor output to a value that mC can handle.
For example you can amplify it, you digitize it and send it with SPI, I2C etc...
3. How you want to control it? With MOS, Triac, SSR?
What control method do you want to use? something easy like On-Off, something more complex like PID or something extreme like Model Predictive?
4. You already choose what you want, cool
How to start building it.
A. Separate it to individual blocks
B. Test each block if behaves as you would like
C. Debug them
D. Combine them
For your application the blocks are:
Controlling heating element
Reading Temperature
Controlling screen
Get input from rotary encoder.
Lets view temperature measurement:
You make a circuit and feeding it on mC which displays it to Serial for ex.
Does mC readings match nozzle temperature? there is steady state error or error goes higher on higher temperatures?
Is temperature accuracy enough for your application?
If you have problems you start solving them 1 by 1.
Lets see screen.
Can you make your mC to display something on this screen?
Can you design your UI on this screen?
How it will look like?
Does screen needs too many pins from mC?
And you continue with the rest.
There are tons of DIY soldering irons on the web, you can build an iron better than the most expensive if you choose carefully what you gonna use and why. Try to act like Dave when he was designing uCurrent
PS. It is very important to make a full plan on your mind. With experience you will be able to make better plans but you need practice on that.
Good luck!