diff --git a/include/pybind11/gil_safe_call_once.h b/include/pybind11/gil_safe_call_once.h
index 25cf59511f..c4ca98adbb 100644
--- a/include/pybind11/gil_safe_call_once.h
+++ b/include/pybind11/gil_safe_call_once.h
@@ -23,11 +23,15 @@ PYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)
 //
 // The following alternative avoids both problems:
 //
-//   PYBIND11_CONSTINIT static py::gil_safe_call_once_and_store<py::object> obj_importer;
-//   auto imported_obj = obj_importer.get_stored([]() { return py::module_::import("module_name");
-//   });
+//   PYBIND11_CONSTINIT static py::gil_safe_call_once_and_store<py::object> storage;
+//   auto &imported_obj = storage // Do NOT make this `static`!
+//       .call_once_and_store_result([]() {
+//           return py::module_::import("module_name");
+//       })
+//       .get_stored();
 //
-// The `get_stored()` argument is meant to be a callable that makes Python C API calls.
+// The `call_once_and_store_result()` argument is meant to be a callable that
+// makes Python C API calls.
 //
 // `T` can be any C++ type, it does not have to be a Python type.
 template <typename T>
@@ -35,7 +39,7 @@ class gil_safe_call_once_and_store {
 public:
     // PRECONDITION: The GIL must be held when `get_stored()` is called.
     template <typename Callable>
-    T &get_stored(Callable &&fn) {
+    gil_safe_call_once_and_store &call_once_and_store_result(Callable &&fn) {
         if (!is_initialized_.load(std::memory_order_acquire)) {
             gil_scoped_release gil_rel;
             std::call_once(once_flag_, [&] {
@@ -44,6 +48,12 @@ class gil_safe_call_once_and_store {
                 is_initialized_.store(true, std::memory_order_release);
             });
         }
+        return *this;
+    }
+
+    // This must only be called after `call_once_and_store()` was called.
+    T &get_stored() const {
+        assert(is_initialized_.load(std::memory_order_relaxed));
         PYBIND11_WARNING_PUSH
 #if !defined(__clang__) && defined(__GNUC__) && __GNUC__ < 5
         // Needed for gcc 4.8.5
@@ -57,7 +67,7 @@ class gil_safe_call_once_and_store {
     PYBIND11_DTOR_CONSTEXPR ~gil_safe_call_once_and_store() = default;
 
 private:
-    alignas(T) char storage_[sizeof(T)] = {};
+    alignas(T) mutable char storage_[sizeof(T)] = {};
     std::once_flag once_flag_ = {};
     std::atomic<bool> is_initialized_ = {};
 };
diff --git a/include/pybind11/numpy.h b/include/pybind11/numpy.h
index c5322cb67b..40f988fdff 100644
--- a/include/pybind11/numpy.h
+++ b/include/pybind11/numpy.h
@@ -207,8 +207,8 @@ struct npy_api {
     };
 
     static npy_api &get() {
-        PYBIND11_CONSTINIT static gil_safe_call_once_and_store<npy_api> imported_api;
-        return imported_api.get_stored(lookup);
+        PYBIND11_CONSTINIT static gil_safe_call_once_and_store<npy_api> storage;
+        return storage.call_once_and_store_result(lookup).get_stored();
     }
 
     bool PyArray_Check_(PyObject *obj) const {
@@ -645,10 +645,13 @@ class dtype : public object {
 
 private:
     static object &_dtype_from_pep3118() {
-        PYBIND11_CONSTINIT static gil_safe_call_once_and_store<object> imported_obj;
-        return imported_obj.get_stored([]() {
-            return detail::import_numpy_core_submodule("_internal").attr("_dtype_from_pep3118");
-        });
+        PYBIND11_CONSTINIT static gil_safe_call_once_and_store<object> storage;
+        return storage
+            .call_once_and_store_result([]() {
+                return detail::import_numpy_core_submodule("_internal")
+                    .attr("_dtype_from_pep3118");
+            })
+            .get_stored();
     }
 
     dtype strip_padding(ssize_t itemsize) {