diff --git a/src/v/rpc/rpc_server.cc b/src/v/rpc/rpc_server.cc
index 2889e36ecb22..19e5cbb99414 100644
--- a/src/v/rpc/rpc_server.cc
+++ b/src/v/rpc/rpc_server.cc
@@ -143,7 +143,15 @@ ss::future<> rpc_server::dispatch_method_once(
                    */
                   reply_buf.set_version(transport_version::max_supported);
                   return send_reply_skip_payload(ctx, std::move(reply_buf))
-                    .then([ctx] { ctx->signal_body_parse(); });
+                    .then_wrapped([ctx](ss::future<> f) {
+                        // If the connection is closed then this can be an
+                        // exceptional future.
+                        if (f.failed()) {
+                            ctx->body_parse_exception(f.get_exception());
+                        } else {
+                            ctx->signal_body_parse();
+                        }
+                    });
               }
               auto it = std::find_if(
                 _services.begin(),
@@ -169,7 +177,15 @@ ss::future<> rpc_server::dispatch_method_once(
                   reply_buf.set_version(ctx->get_header().version);
                   reply_buf.set_status(s);
                   return send_reply_skip_payload(ctx, std::move(reply_buf))
-                    .then([ctx] { ctx->signal_body_parse(); });
+                    .then_wrapped([ctx](ss::future<> f) {
+                        // If the connection is closed then this can be an
+                        // exceptional future.
+                        if (f.failed()) {
+                            ctx->body_parse_exception(f.get_exception());
+                        } else {
+                            ctx->signal_body_parse();
+                        }
+                    });
               }
 
               method* m = it->get()->method_from_id(method_id);
diff --git a/src/v/rpc/service.h b/src/v/rpc/service.h
index 018a2dbf40c4..6d4360b794c7 100644
--- a/src/v/rpc/service.h
+++ b/src/v/rpc/service.h
@@ -17,6 +17,7 @@
 #include "seastarx.h"
 #include "ssx/sformat.h"
 
+#include <seastar/core/future.hh>
 #include <seastar/core/reactor.hh>
 #include <seastar/core/scheduling.hh>
 
@@ -81,6 +82,14 @@ struct service::execution_helper {
       method_info method,
       Func&& f) {
         return ctx.permanent_memory_reservation(ctx.get_header().payload_size)
+          .handle_exception([&ctx](const std::exception_ptr& e) {
+              // It's possible to stop all waiters on a semaphore externally
+              // with the semaphore's `broken` method. In which case
+              // `permanent_memory_reservation` will return an exception.
+              // We intercept it here to avoid a broken promise.
+              ctx.body_parse_exception(e);
+              return ss::make_exception_future(e);
+          })
           .then([f = std::forward<Func>(f), method, &in, &ctx]() mutable {
               return parse_type<Input, Codec>(in, ctx.get_header())
                 .then_wrapped([f = std::forward<Func>(f),