SQL Server sp_describe_first_result_set: find user defined types
This appears not to work as advertised. Temporary tables are disallowed, but table variables should work just fine. Alias types are a bit of an edge case, so perhaps a bug crept in here unnoticed. If it is a blocker for you, open a support case with Microsoft.
There aren't any perfect workarounds (that I am aware of). One of the best ones is to create a wrapper procedure that uses WITH RESULT SETS to define the output shape:
CREATE TYPE dbo.udtTest FROM nvarchar(123) NOT NULL;
GO
CREATE OR ALTER PROCEDURE dbo.P AS
SET NOCOUNT ON;
DECLARE @T TABLE (udt dbo.udtTest);
INSERT @T VALUES (N'Banana');
SELECT T.udt FROM @T AS T;
GO
-- No user type info
EXECUTE sys.sp_describe_first_result_set 
    @tsql = N'EXECUTE Sandpit.dbo.P;', 
    @parameters = NULL, 
    @browse_information_mode = 0;

-- Wrapper for dbo.P
CREATE OR ALTER PROCEDURE dbo.P_Wrapper AS
SET NOCOUNT ON;
EXECUTE dbo.P 
    WITH RESULT SETS ((udt dbo.udtTest NOT NULL));
GO
-- Works!
EXECUTE sys.sp_describe_first_result_set 
    @tsql = N'EXECUTE dbo.P_Wrapper;', 
    @parameters = NULL, 
    @browse_information_mode = 0;

This may or may not be convenient or practical for you. It's probably the best we can do until the bug (?) is fixed, or Microsoft extend CREATE PROCEDURE syntax to include WITH RESULT SETS, as we have been asking for a long time now.