Season shoulder roast cubes with salt and pepper while heating oil in Instant Pot set to Sauté.

Brown roast cubes on two sides (about 4-5 minutes). Add onion and garlic and sauté; stirring occasionally for 2-3 minutes. Add beef broth and thyme, secure lid and set to Meat/Stew setting (will take about 35 minutes to cook).

Prepare rolls by cutting each group of 12 horizontally to create a top and bottom layer. Place both bottom layers on a baking sheet and shingle 6 slices of cheese on each.

Release steam from Instant Pot and remove lid. Remove cooked roast cubes and place in a bowl to cool for 10 minutes. Set Instant Pot to Sauté for 10 minutes to reduce cooking liquid.

Preheat oven to 300°F. Strain reduced cooking liquid, reserving for jus. Skim fat from top and keep warm.

Shred roast cubes and spread evenly over top the cheese on each group of rolls. Place the top layer atop the shredded beef. Brush roll tops with melted butter and sprinkle the center of each bun with a pinch of coarse salt.

Bake15 minutes and serve with jus. Pull sliders apart or cut and serve separately.