Preheat grill/smoker to 325°F with indirect heat and add hickory chunks.
Trim and season the sirloin roast with the herb blend.
Dissolve bouillon cubes in 6 cups water inside a pan on the grill.
Place roast on a rack over the jus, insert thermometer, and smoke until 125–130°F.
Remove and chill the roast and jus for at least 3 hours or overnight.
Skim fat from chilled jus, then simmer in a crockpot or saucepan.
Slice peppers and sauté with oil and seasoning until tender.
Thinly slice the chilled beef.
Dip beef slices in hot jus for 1 minute before serving.
Split rolls, layer with beef, sautéed peppers, and giardiniera, then dunk entire sandwich in jus if desired.
