diff --git a/Lib/email/_header_value_parser.py b/Lib/email/_header_value_parser.py
index 5b653f66c18554..ce4776cfc3e20a 100644
--- a/Lib/email/_header_value_parser.py
+++ b/Lib/email/_header_value_parser.py
@@ -1513,16 +1513,22 @@ def get_obs_local_part(value):
                 raise
             token, value = get_cfws(value)
         obs_local_part.append(token)
-    if (obs_local_part[0].token_type == 'dot' or
-            obs_local_part[0].token_type=='cfws' and
-            obs_local_part[1].token_type=='dot'):
+    if not obs_local_part:
         obs_local_part.defects.append(errors.InvalidHeaderDefect(
-            "Invalid leading '.' in local part"))
-    if (obs_local_part[-1].token_type == 'dot' or
-            obs_local_part[-1].token_type=='cfws' and
-            obs_local_part[-2].token_type=='dot'):
-        obs_local_part.defects.append(errors.InvalidHeaderDefect(
-            "Invalid trailing '.' in local part"))
+            "abandoned parse; truncated value?"))
+    else:
+        if (obs_local_part[0].token_type == 'dot'
+            or (obs_local_part[0].token_type=='cfws'
+                and len(obs_local_part) > 1
+                and obs_local_part[1].token_type=='dot')):
+            obs_local_part.defects.append(errors.InvalidHeaderDefect(
+                "Invalid leading '.' in local part"))
+        if (obs_local_part[-1].token_type == 'dot'
+            or (obs_local_part[-1].token_type=='cfws'
+                and len(obs_local_part) > 1
+                and obs_local_part[-2].token_type=='dot')):
+            obs_local_part.defects.append(errors.InvalidHeaderDefect(
+                "Invalid trailing '.' in local part"))
     if obs_local_part.defects:
         obs_local_part.token_type = 'invalid-obs-local-part'
     return obs_local_part, value
diff --git a/Lib/test/test_email/test__header_value_parser.py b/Lib/test/test_email/test__header_value_parser.py
index bdb0e55f21069f..7327f91d1224af 100644
--- a/Lib/test/test_email/test__header_value_parser.py
+++ b/Lib/test/test_email/test__header_value_parser.py
@@ -2588,6 +2588,22 @@ def test_get_msg_id_empty(self):
         with self.assertRaises(errors.HeaderParseError):
             parser.get_msg_id('')
 
+    def test_get_msg_id_square_brackets(self):
+        # gh-105802: test for broken Microsoft Message-Id with square brackets.
+        msg_id = self._test_get_x(
+            parser.get_msg_id,
+            '<[TeRriBlyLongBase64==@microsoft.com]>',
+            '<', # sic
+            '<', # sic
+            # This also triggers
+            # ObsoleteHeaderDefect('obsolete id-left in msg-id')
+            # and InvalidHeaderDefect('msg-id with no id-right')
+            [errors.ObsoleteHeaderDefect, errors.InvalidHeaderDefect,
+             errors.InvalidHeaderDefect],
+            '[TeRriBlyLongBase64==@microsoft.com]>',
+            )
+        self.assertEqual(msg_id.token_type,'msg-id')
+
     def test_get_msg_id_valid(self):
         msg_id = self._test_get_x(
             parser.get_msg_id,
diff --git a/Misc/NEWS.d/next/Library/2023-08-19-13-48-11.gh-issue-105802.0p286F.rst b/Misc/NEWS.d/next/Library/2023-08-19-13-48-11.gh-issue-105802.0p286F.rst
new file mode 100644
index 00000000000000..a3da1ecebd8b5a
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2023-08-19-13-48-11.gh-issue-105802.0p286F.rst
@@ -0,0 +1,2 @@
+In :mod:`email` library, avoid another IndexError in Message-Id parsing for
+improper tokens; fixes <[broken@microsoft.com]> case