I'd say that is probably typical of what you'll get in am EAP setting but you could try a different counselor if you like. EAP is like triage, their goal is to get you back to work so you can be productive. If you're productive but still depressed, that's okay as long as you're not missing work or etc..

Going through the EAP is a show of good faith so that if you decide you want to do longer term therapy with someone outside EAP, it should get approved without a problem. (Depends greatly on what type of insurance you have. )

Maybe if you tell the counselor that you're thinking about doing longer term therapy as a follow up to EAP, they might be able to help you understand what you want to get out of therapy, what type of therapist you'd like to see, goals for therapy etc..

I'm not against EAP, it has its place. But if you've been depressed for two years, 4 sessions worth EAP is unlikely to fix that. I don't know what you're problem is (probably don't need to know) but it sounds like you're looking for a more in depth exploration than you can get from EAP. Best of luck to you!