Place figs in a small microwavable bowl and cover with port. Cover the bowl and microwave on High for 3 minutes.

Heat 2 teaspoons oil in a small saucepan over medium heat. Add onion and cook, stirring, until soft and translucent, 4 to 6 minutes. Add broth, thyme, bay leaf and the fig-port mixture. Bring to a boil and cook until reduced by half, 10 to 12 minutes. Season with vinegar, 1/4 teaspoon salt and pepper. Set aside.

Sprinkle both sides of pork medallions with the remaining 1/4 teaspoon salt and pepper and dredge lightly with flour, shaking off the excess.

Heat the remaining 1 tablespoon oil in a large nonstick skillet over medium-high heat. Add the medallions and cook until browned, 2 to 3 minutes per side. Add the reserved fig-port sauce; bring to a simmer and cook until the pork is cooked, but still a little pink in the center, about 2 minutes. The sauce should be syrupy. If not, remove the medallions with a slotted spoon to a platter and tent with foil to keep warm. Boil the sauce until it's reduced and syrupy. Discard the bay leaf. Serve the sauce over the medallions.

Note: What differentiates tawny from ruby port is that tawny is aged in oak, turning its ruby color toward brown.