Bring a large pot of water to a boil; when boiling, salt the water and cook pasta al dente; drain pasta, but reserve ½ cup pasta cooking liquid.
Preheat a large nonstick skillet over medium-high heat with 3 tablespoons oil; add in eggplant; cook, stirring occasionally, until brown, about 5-6 minutes.
Remove the eggplant from the skillet to a plate and cover with foil to keep warm.
Return the skillet to the stove; add in the remaining 2 tablespoons oil; add in the chicken and cook to lightly brown, about 4-5 minutes.
Add in the onions and garlic; return the eggplant to the skillet, season with salt, pepper, and crushed red pepper flakes; continue to cook 3-4 minutes.
Add in white wine and chicken stock; bring to a simmer; cook for 3-4 minutes.
Add in the cherry tomatoes and pasta water; cook until the tomatoes begin to burst.
Add in the parsley and cooked pasta; toss to coat, and cook for 1-2 minutes or until the sauce tightens up around the pasta.
Turn off the heat; add in grated Parmigiano-Reggiano; toss to coat the spaghetti.
Serve warm with crusty bread.