As lenoch stated, a framework isn't a good way to understand to code and finding exploits, especially large frameworks such as laravel as they have many eyes on it to harden the code. Learn basic php scripting and databases, how PHP speaks with databases and commen mistakes website developers make that can open up SQLi, XSS, RFI, LFI and others. A good foundation of PHP will also make utilizing frameworks much easier.
Good luck on your journey and I think 3 years is a decent time frame to explore what you want. BTW, welcome to EvilZone.
+1 Lenoch for the valuable input