What we may have here is a stranded object complement in an agentless passive clause.

X burned language deep into my memory.

Language is burned deep into my memory (by X).

Bruce gives some helpful examples of verbs that routinely take adjective object complements. 

The kids painted the wall black. (complex transitive, with "black" as object complement.) The wall was painted black by the kids. (passive version.) The wall was painted black. (Agentless passive. Black feels like a stranded adjective.)

"Deep," though, seems to show up in non-passive clauses. "Still waters run deep." "Her remarks cut deep." (Perhaps I was cut deep by her remarks?)

The big question might be what burns language deep into our memories. Is that an accurate or helpful metaphor for the process? The mind allows itself to be burned by language? 

To me, it makes more sense to say that much of language has become routinized. There is an evolutionary advantage to routinization in so many human activities. The language has been learned, becomes routinized, and then resists being brought to conscious attention, especially when the value of conscious attention has been denigrated and people have very little experience with it.