1. Read Technical Documentation.
If you write software, read about new languages, or techniques. If you design buildings, learn about new techniques, materials.
2. Read Context Documentation.
Understand your customer, when you see the pain points of customers, you can understand better how to solve the problems they are experiencing.
3. Think Wider.
If you are trying to solve a problem, try to solve it in more than one way. Aim to meet the same end result with each option. Look at how each can work for and against your end goal.
4. Be social, share
Talk to other engineers, particularly others that are always furthering their knowledge, sometimes you'll find that they understood a subject differently than you, which is good, this gives you another view. Also if you share stuff you build, you might find others are interested in helping out, and show you new ways to solve your current problems.
5. Test your assumptions.
Create a hypothesis about everything you do, and then prove your hypothesis is correct. Do this one day a week. Whether its writing code, simulating the tensile strength of a set of materials you're considering using. Find ways to prove that your understanding of the system is right, even if you are 'certain' you're right. See if you can 'break' what you thought was a certainty.
Good luck, do you have any other ideas of How to think more like an engineer? Share them in the comments.