Pour olive oil into a large frying pan over medium-high heat. Add pancetta and cook, stirring occasionally, until it begins to get crisp and brown, 4 to 5 minutes. With a slotted spoon, transfer pancetta to a bowl.
Add peppers, onion, garlic, thyme, and 1/2 tsp. salt to pan, and cook, stirring often, until vegetables begin to soften, 7 to 10 minutes. Lower heat to medium-low and cook, stirring occasionally, until very soft, about 25 minutes longer.
Add chicken broth, vinegar, tomatoes, and cooked pancetta to pan. Increase heat to medium-high, and boil, stirring often, until liquid is very slightly reduced and thickened, 8 to 10 minutes. Stir in olives if using, and season to taste with pepper and more salt.
Meanwhile, poach eggs (recipe follows).
Spoon pipérade into 2 wide, shallow bowls, and nestle 1 or 2 poached eggs in each serving.
Perfect Poached Eggs
Put about 3 in. water in a wide pan; bring to a boil over high heat. With a slotted spoon, quickly and gently immerse eggs in the shell, 1 at a time, for 8 seconds, then lift out.
Pour out all but 1 in. of water from pan; reduce heat so bubbles on pan bottom pop to the surface only occasionally. Crack eggs 1 at a time, and, holding shell close to the surface of the water, break it open to let egg slide gently into water. Cook to desired doneness (poke gently with a spoon to check), 3 to 4 minutes for soft-poached eggs.
With slotted spoon, lift eggs 1 at a time from water.
Note: Nutrition analysis is per serving.