diff --git a/cwltool/command_line_tool.py b/cwltool/command_line_tool.py
index b11bb4bc3..d249c0200 100644
--- a/cwltool/command_line_tool.py
+++ b/cwltool/command_line_tool.py
@@ -1495,8 +1495,21 @@ def collect_output(
                             )
                         primary["format"] = format_eval
                 else:
-                    for primary in aslist(result):
-                        primary["format"] = format_field
+
+                    def recursively_insert(j_dict: Any, key: Any, val: Any) -> Any:
+                        """Recursively insert a value into any dictionary."""
+                        if isinstance(j_dict, MutableSequence):
+                            return [recursively_insert(x, key, val) for x in j_dict]
+                        if isinstance(j_dict, MutableMapping):
+                            if j_dict.get("class") == "File":
+                                j_dict[key] = val
+                            else:
+                                return {
+                                    x: recursively_insert(y, key, val) for x, y in j_dict.items()
+                                }
+                        return j_dict
+
+                    result = recursively_insert(result, "format", format_field)
             # Ensure files point to local references outside of the run environment
             adjustFileObjs(result, revmap)
 
diff --git a/tests/output_2D_file_format.cwl b/tests/output_2D_file_format.cwl
new file mode 100644
index 000000000..621111061
--- /dev/null
+++ b/tests/output_2D_file_format.cwl
@@ -0,0 +1,29 @@
+#!/usr/bin/env cwl-runner
+cwlVersion: v1.0
+
+class: CommandLineTool
+
+baseCommand: 'true'
+
+requirements:
+  InlineJavascriptRequirement: {}
+
+inputs: {}
+
+outputs:
+  output_array:
+    type: {"type": "array", "items": {"type": "array", "items": "File"}}
+    outputBinding:
+      outputEval: |
+        ${
+          var out2d = [];
+          for (var i = 0; i < 2; i++) {
+            var out1d = [];
+            for (var j = 0; j < 2; j++) {
+              out1d.push({"class": "File", "location": "../../filename.txt"});
+            }
+            out2d.push(out1d);
+          }
+          return out2d;
+        }
+    format: some_format
diff --git a/tests/test_2D.py b/tests/test_2D.py
new file mode 100644
index 000000000..87d16ccf0
--- /dev/null
+++ b/tests/test_2D.py
@@ -0,0 +1,21 @@
+from pathlib import Path
+
+from .util import get_data, get_main_output
+
+
+def test_output_2d_file_format(tmp_path: Path) -> None:
+    """A simple test for format tag fix for 2D output arrays."""
+
+    # still need to create 'filename.txt' as it is needed in output_2D_file_format.cwl
+    (tmp_path / "filename.txt").touch()
+    commands = [
+        "--cachedir",
+        str(tmp_path / "foo"),  # just so that the relative path of file works out
+        "--outdir",
+        str(tmp_path / "out"),
+        get_data("tests/output_2D_file_format.cwl"),
+    ]
+
+    error_code, _, stderr = get_main_output(commands)
+
+    assert error_code == 0, stderr