Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Rub red pepper, yellow pepper, and onion slices with vegetable oil to prevent sticking.
Grill on the preheated grill until blackened on both sides, about 5 minutes per side.
Put grilled peppers in a paper bag, seal tightly, let stand for 10 minutes. Remove peppers; discard skins, seeds, and stems. Chop peppers and onion slices roughly.
Place peppers, onions, parsley, bread, lemon juice, garlic, and thyme in a blender; pulse until roughly chopped. Drizzle olive oil into running blender until mixture becomes smooth, 2 to 3 minutes. Season with salt, stir to combine.