Whisk together the broth, oyster sauce, chile paste, and cornstarch in a small bowl.
Heat the peanut oil in a large skillet over medium high heat.
Add shrimp and peanuts and cook, stirring, until the shrimp are just barely cooked (2 - 3 minutes). Transfer them to a plate.
Heat the sesame oil in the skillet, and saute the bell pepper until just barely tender (about 3 minutes). Then add the garlic and ginger to the skillet with the bell peppers and cook, stirring, until fragrant (about 1 minute).
Add the broth mixture to the pan with the pepper mixture. Bring to boil. When boiling, add the shrimp and peanuts and simmer until the sauce has thickened, about 1 minute. Make sure the shrimp are done (but not overcooked).