Brush olive oil over brisket. Combine rub ingredients; rub over both sides of beef. Securely wrap in plastic wrap; place on a rimmed baking sheet. Refrigerate overnight or up to 2 days. Meanwhile, in a small saucepan, combine mop sauce ingredients. Simmer 15 minutes, stirring occasionally. Refrigerate until ready to grill.
Soak hickory and mesquite chips or pellets; add to smoker according to manufacturer's directions. Heat to 225°. Unwrap brisket; discard plastic wrap. Place brisket in smoker fat side up; smoke 2 hours. Brush generously with mop sauce; turn meat. Smoke 2 more hours; brush generously with mop sauce again. Wrap brisket securely in heavy-duty aluminum foil; smoke until a thermometer inserted in beef reads 190°, about 4-5 more hours.
Let stand 20-30 minutes before slicing; cut diagonally across the grain into thin slices.
Editor’s Note: This is a fresh beef brisket, not corned beef.