1. Melt butter in a large saucepan; add diced ham, green onions, and minced garlic; cooking over low heat until garlic is fragrant.
2. Add the mashed potatoes, broth, milk, peas, and thyme, stirring to combine.
3. Turn heat up to medium and bring to a boil, immediately reducing heat to low, then simmer slowly for 10 minutes or until soup thickens, season with salt and pepper.
4. Spoon into 4 broiler-safe bowls. Scatter the torn dinner rolls and sprinkle with the shredded Cheddar cheese.
5. Place bowls on a broiler pan 6 inches under broiler turned on high, and broil 1 to 3 minutes or until top bubbles and gets golden brown.
6. Remove and let cool slightly. Serves 4.