Whisk yogurt, chicken broth, lemon juice, Dijon mustard, garlic, and 1 teaspoon black pepper together in a bowl until dressing is smooth.
Bring a large pot of lightly salted water to a boil; add penne and cook, stirring occasionally, until tender yet firm to the bite, about 8 minutes. Drain and rinse under cold water until pasta is slightly cooled.
Preheat oven to 450 degrees F (230 degrees C).
Toss shrimp and 2 tablespoons olive oil together in a bowl; season with salt and pepper. Transfer to a glass baking dish.
Bake in the preheated oven until shrimp are bright pink and cooked through, 10 to 12 minutes.
Toss pasta with dressing in a bowl. Add shrimp and scallions; season with 1 teaspoon kosher salt and more pepper. Garnish pasta salad with Cheddar cheese and lemon slices.