Kelley's on Park Place @ 45 has one on the menu, on Texas Toast. There are other locations but none in the city limits of Houston. $6.99 on the menu I have from several years ago; probably gone up but Kelley's portions are humongous.
Harry's on Tuam serves Turkey and Dressing on Monday and Thursday; Cleburne Cafeteria on Bissonnet serves it on Sunday and Thursday; both would undoubtedly offer Mashed Pots as a side and you might be able to engineer a sandwich on your own. Cleburne is pricey for a cafeteria but portions are large, too. You might try Dinner Bell Cafeteria over close to UH also for T&D.
3606 Bissonnet St, Houston, TX 77005
Dinner Bell Cafeteria
6525 Lawndale St, Houston, TX 77023