Heat the oil in a large, deep skillet with a tight-fitting lid over medium-high heat. Add chicken and cook for 2 minutes per side or until golden brown.
Add broth and wine (or juice/vinegar) then add garlic and sliced onion over the top. Reduce skillet heat to medium-low then sprinkle flour, salt, and pepper evenly over the sliced onion top (use a sieve to tap the flour if you’re uncertain you'll avoid lumps).
Cover and simmer chicken for 40 to 45 minutes. Meanwhile, prepare rice. When chicken is cooked through, remove from skillet, set aside and keep warm.
Whisk evaporated milk into the pan juices; cook for 10 minutes or until sauce is reduced to desired thickness.
Return chicken to the skillet and turn to coat in the sauce; heat through. Serve over hot rice.