diff --git a/bindings/pybind11_ext/numpy_dtypes_user.h b/bindings/pybind11_ext/numpy_dtypes_user.h
index 629342b3ea5b..1341881d82ec 100644
--- a/bindings/pybind11_ext/numpy_dtypes_user.h
+++ b/bindings/pybind11_ext/numpy_dtypes_user.h
@@ -466,16 +466,16 @@ class dtype_user : public object {
   }
 
   /// Defines a constructor.
-  template <typename ... Args>
+  template <typename ... Args, typename ... Extra>
   dtype_user& def(
-      detail::initimpl::constructor<Args...>&&, const char* doc = "") {
+      detail::initimpl::constructor<Args...>&&, Extra&&... extra) {
     // See notes in `add_init`.
     // N.B. Do NOT use `Class*` as the argument, since that may incur recursion.
     add_init([](object py_self, Args... args) {
       // Old-style. No factories for now.
         Class* self = DTypePyObject::load_raw(py_self.ptr());
       new (self) Class(std::forward<Args>(args)...);
-    }, doc);
+    }, detail::type_pack<Args...>{}, std::forward<Extra>(extra)...);
     return *this;
   }
 
@@ -607,8 +607,8 @@ class dtype_user : public object {
   }
 
   // Adds constructor. See comments within for explanation.
-  template <typename Func>
-  void add_init(Func&& f, const char* doc) {
+  template <typename Func, typename... Extra, typename... Args>
+  void add_init(Func&& f, detail::type_pack<Args...>, Extra&&... extra) {
     // Do not construct this with the name `__init__` as `pybind11`s
     // constructor implementations via `cpp_function` are rigidly fixed to
     // its instance registration system (which we don't want).
@@ -620,10 +620,10 @@ class dtype_user : public object {
     if (!d.contains("__init__")) {
       auto init = self().attr("_dtype_init");
       auto func = cpp_function(
-          [init](handle self, args args, kwargs kwargs) {
+          [init](handle self, Args... args) {
             // Dispatch.
-            init(self, *args, **kwargs);
-          }, is_method(self()), doc);
+            init(self, std::forward<Args>(args)...);
+          }, is_method(self()), std::forward<Extra>(extra)...);
       self().attr("__init__") = func;
     }
   }
diff --git a/bindings/pydrake/symbolic_py.cc b/bindings/pydrake/symbolic_py.cc
index 62ea6ce03fec..363f32f446fc 100644
--- a/bindings/pydrake/symbolic_py.cc
+++ b/bindings/pydrake/symbolic_py.cc
@@ -61,8 +61,9 @@ PYBIND11_MODULE(symbolic, m) {
           var_doc.Type.RANDOM_EXPONENTIAL.doc);
 
   var_cls
-      .def(py::init<const string&, Variable::Type>(), py::arg("name"),
-          py::arg("type") = Variable::Type::CONTINUOUS, var_doc.ctor.doc_2args)
+      .def(py::init<const string&, Variable::Type>(),
+          py::arg("name"), py::arg("type") = Variable::Type::CONTINUOUS,
+          var_doc.ctor.doc_2args)
       .def("get_id", &Variable::get_id, var_doc.get_id.doc)
       .def("get_type", &Variable::get_type, var_doc.get_type.doc)
       .def("__str__", &Variable::to_string, var_doc.to_string.doc)
@@ -209,7 +210,7 @@ PYBIND11_MODULE(symbolic, m) {
   expr_cls  // BR
       .def(py::init<>(), doc.Expression.ctor.doc_0args)
       .def(py::init<double>(), doc.Expression.ctor.doc_1args_d)
-      .def(py::init<const Variable&>(), doc.Expression.ctor.doc_copy)
+      .def(py::init<const Variable&>(), doc.Expression.ctor.doc_1args_var)
       // Casting
       .def_loop(py::dtype_method::implicit_conversion<Variable, Expression>())
       // Methods