In a small bowl, whisk together the sauce ingredients: 1/4 cup low-sodium chicken stock, 1 tablespoon chili paste, 1 tablespoon soy sauce, 1 tablespoon rice vinegar, 1 tablespoon oyster sauce, 1 teaspoon tomato paste, and 1 teaspoon grated garlic. Set the sauce aside.
Pat the 1 pound raw shrimp dry with paper towels. Place the shrimp in a large bowl, sprinkle 3 tablespoons cornstarch over them, and toss lightly so each shrimp is evenly coated. Shake off any excess cornstarch.
Heat a large skillet or wok over medium-high heat until hot. Add 2 tablespoons of the olive oil and heat until very hot and shimmering.
Add the shrimp to the pan in a single layer (cook in batches if necessary to avoid overcrowding). Sear without moving for about 3 minutes, until the bottoms are lightly browned. Flip the shrimp and cook another 3 minutes, until they are plump and opaque.
Remove the seared shrimp to a plate and set aside.
Add the remaining 1 tablespoon olive oil to the same skillet. When the oil is shimmering, add 2 cups cut (1" pieces) fresh green beans. Cook, stirring occasionally, for 4–5 minutes, until the beans begin to blister and brown.
Pour the prepared Hunan sauce into the skillet with the green beans. Bring to a simmer and cook, stirring, for 2–3 minutes, until the sauce is bubbling and slightly thickened.
Return the seared shrimp to the skillet and toss to coat with the sauce. Cook for about 1 minute more, until the shrimp are heated through and evenly glazed.
Remove from heat and serve immediately, garnished with sliced green onion and sesame seeds. For a heartier meal, serve over cooked white rice.