Cook spaghetti in salted boiling water to al dente, about 9-11 minutes. Reserve 1 cup pasta water, drain and set aside.
Whisk egg yolks, heavy cream, and parmesan in a medium bowl. Slowly add ½ cup warm reserved pasta water while whisking to temper the eggs, then set aside.
In a large skillet over medium heat, cook diced bacon for 15-18 minutes, stirring often until crispy. Remove bacon with a slotted spoon and drain excess fat, leaving 2 tablespoons in the skillet.
Toss chicken strips and shrimp with olive oil, Italian seasoning, salt, and black pepper in a large bowl.
Increase skillet heat to medium-high and cook the chicken for 3-4 minutes per side until golden and internal temperature reaches 165°F. Remove chicken and set aside.
Add shrimp to skillet and cook 1-2 minutes per side until lightly golden and fully cooked. Remove and set aside with chicken.
Add red bell pepper strips, diced onion, and minced garlic to the skillet. Cook 3-4 minutes until vegetables are crisp-tender and garlic is fragrant. Remove bell peppers, leaving onions and garlic to cook further. Set peppers aside.
Lower heat to medium-low. Slowly pour in egg and cream mixture while whisking constantly. Cook 2-3 minutes until sauce bubbles and thickens to coat the back of a spoon.
Return red bell pepper strips and cooked spaghetti to the skillet. Toss to coat noodles in the carbonara sauce.
Add crispy bacon pieces to the skillet and toss with spaghetti and sauce.
Top the pasta with cooked chicken strips and shrimp.
Garnish with chopped fresh parsley and serve immediately.