Heat butter and olive oil in a large saucepan over medium heat. Cook and stir onion and garlic in hot butter-oil mixture until tender but not browned, about 5 minutes. Add milk, bouillon, oregano, salt, and pepper to onion mixture; bring to a boil. Reduce heat to medium and cook sauce for 5 minutes.
Whisk together cold water and cornstarch in a small bowl until smooth. Mix cornstarch mixture and chicken chunks into sauce; cook until heated through and thickened, about 5 minutes.
Meanwhile, bring a large pot of lightly salted water to a boil. Cook linguine in boiling water until tender yet firm to the bite, about 11 minutes; drain.
Reduce heat under the saucepan with sauce to low. Add lemon juice, parsley, and lemon zest; cook until heated through, 1 to 2 minutes. Add cooked linguine, toss to coat, and transfer to a serving bowl; top with Parmesan cheese.
