Pour chicken broth into a multi-functional electric pressure cooker. Place a steamer rack into the pot. Add yam and potato; sprinkle pink salt on top. Close and lock the lid. Turn valve to Seal. Select high pressure according to manufacturer's instructions; set timer for 8 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove lid. Remove yam, potato, and rack. Strain liquid into a glass measuring cup and reserve. Return yam and potato to pot. Add milk and butter; mash using a potato masher until smooth. Scrape mashed potato topping into a bowl using a silicone spatula.
Preheat the oven to 350 degrees F (175 degrees C).
Select Saute function on the pressure cooker. Heat oil on high mode. Add onion and garlic; saute until slightly tender, 1 to 2 minutes. Add ground beef, salt, and pepper. Cook and stir until filling is well combined, 2 to 3 minutes. Add mushrooms; saute until starting to soften, about 1 minute.
Stir corn, peas, broccoli, carrot, and celery into the pot with the filling. Pour in reserved potato liquid. Close and lock the lid. Set pot to Manual function. Select low pressure according to manufacturer's instructions; set timer for 3 minutes. Allow 5 to 10 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove lid. Strain out excess liquid and discard; return filling to pot. Set pot to Saute mode.
Dissolve gravy mix in just enough water to dissolve the powder; add to the filling in the pot. Cook and stir until gravy thickens, about 2 minutes. Transfer filling to a baking dish and cover with the mashed topping. Sprinkle Cheddar cheese on top.
Bake in the preheated oven until cheese is melted, about 10 minutes.
Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Broil shepherd's pie until top is browned, 3 to 5 minutes. Let sit for 5 minutes before serving.