Bring a large pot of salted water to a boil and cook fettuccine according to package directions until al dente.
In a food processor, blend feta cheese, Greek yogurt, lemon zest, and lemon juice until smooth; set aside for garnish.
Season chicken strips evenly with smoked paprika, garlic powder, salt, and black pepper.
Heat 1 tablespoon of olive oil in a large skillet over high heat; add green beans and sear until charred and tender-crisp, then remove from pan.
Add remaining olive oil to the same skillet and cook chicken over medium-high heat until golden brown and cooked through (165°F), then remove and set aside.
Reduce heat to medium, melt butter in the skillet, and sauté minced garlic for 1 minute until fragrant.
Pour in heavy cream and simmer for 5 minutes, whisking occasionally until slightly reduced.
Whisk in the grated Parmesan cheese until the sauce is smooth and thickened.
Incorporate the cooked pasta and chicken into the Alfredo sauce, tossing to coat thoroughly.
Plate the pasta and top with charred green beans and a dollop of the lemon feta whip.