How to prove my worth in job applications with weak resume

I graduated with a bachelor's of engineering in a top public school. I learned software in my first job, where for a few years I did enterprise Java, some basic SQL and basic frontend. It was definitely a large code base, just no fancy technology behind it. After that, I struggled to find a job and out of desperation accepted an application configuration developer position. Essentially, I work in the services side of the company, doing simple coding and configuration of the product for separate clients. I have always been very aware how this is a step back (even worse considering I didn't start very far ahead to begin with).

But every time I attempt to apply to jobs, I can't get them. I feel like I'm stuck. I feel most employers on the Who's Hiring thread (or anywhere else) probably look at my resume and not see me aligning anywhere close to their requirements. Which I would probably agree to. But at this point I'm also somewhere close to 10 years into my career, so I'm definitely not a junior. I feel like the only jobs I will be able to get are similar to what I've had: basic web developer, not tackling any interesting problems, little potential for growth, and if I'm lucky maybe using some modern technology.

I really just want a job that is willing to accept that I don't have their requirements, but them being okay to letting me pick it up on the job. More than anything, I want to grow my career. I want to work somewhere challenging, where I can problem solve and learn. I am not a bad software developer. If anything, I'm quick to learn and will always end up being the subject matter expert of what I'm working on. I like computer science, which is why I'm also currently enrolled in a computer science masters. I know I'm not dumb. I just don't know how to prove my worth to companies when applying.

Any advice will be very appreciated