Despite its odd appearance at first glance, there are numerous instances online, including several citations in literature, which confirm melted onions' status as a side dish, a culinary equivalent of caramelized onions.
I was obliged to limit the search to "steak with melted onions" because the German dish, as described by the OP, was steak and geschmolzene (melted) Zwiebeln (onions).
According to Google Ngrams, the following phrases are more commonly seen in print: softened onions (blue line), browned onions (red line), sauteed onions (green line), and caramelized onions (orange line); the expression, "melted onions", albeit easily understood, fails to make any mark.
Predictably, the British English corpus fails to register "melted onions" but also, surprisingly, "softened onions". I included the British spelling caramelised to see what the results would be like.
In Google books
- "steak with caramelized onions" yielded 1,080 results
- "steak with fried onions", 435 results
- "steak with sauteed onions", 112 results
However, over the years, I have learned to take Google's search results with a large pinch of salt. It is distinctly possible that these numbers will be significantly different in the near future, if or when Google succeeds in fixing their data that produces these estimated number of results.
The dish, steak with melted onions, produces 112 results but unfortunately, the only excerpt visible is from the recipe book, In a French Kitchen: Tales and Traditions of Everyday Home Cooking in France. (link)
— {STEAK AUX OIGNONS CONFITS} STEAK WITH MELTED ONIONS
I love to quickly sear flank steak for this recipe, which is so simple you'll do it with your eyes closed. Use the steak of your choice, though, and adjust the cooking time accordingly. As for the onions, you'll fall quickly, deeply in love. …
Finally, online we have:
- Peppercorn-Crusted Steak with Melted Onions and Mushrooms (USA)
- Marinated Steak with Melted Onions (Canada)
- Swabian sirloin steak with melted onions, cabbage and homemade Spätzle (Germany)
- Sirloin steak with gravy, melted onions and pan fried potatoes or swabian noodles (Germany)
- "I've had amazing cheese steaks, and I've had crappy cheese steaks. This one was somewhere in-between. The roll it was served in was OK. The steak with melted onions and cheese, was again OK." (N.Carolina, USA)
- Marinated Grilled Steak with Melted Onions (Canada)
- Grilled Beef Steak Sandwich with Melted Onions (Canada)
- Salt & Pepper Crusted Filet Mignon
Melted Onions, Roaring 40’s Blue, Potato Parsnip Puree (Connecticut, USA)
Last but not least, the renowned British food and cookery author Hugh Fearnley-Whittingstall includes the recipe of the following dish:
- Gurnard with melted onions and black olives
So essentially everyone thought that this was a wrong translation from the German "geschmolzene Zwiebeln".
What would be in your opinion the more accurate translation/description? I've not heard the term "melted onions" before, it is easy to understand but I suspect that it is NOT a term used by professional cooks or chefs.