Cook shallot, thyme sprigs, and bay leaf in butter in a 1- to 1 1/2-quart heavy saucepan over moderately low heat, stirring, until shallot is softened, about 2 minutes.
Add dried figs, Port, salt, and pepper and bring to a boil. Simmer, covered, until figs are soft, about 10 minutes. If there is still liquid in saucepan, remove lid and simmer, stirring, until most of liquid is evaporated, 3 to 4 minutes more. Discard bay leaf and thyme sprigs and transfer jam to a bowl. Cool, then stir in minced thyme and salt and pepper to taste.
Put oven rack in middle position and preheat to 350°F.
Halve each baguette slice diagonally, then arrange on a baking sheet and brush tops lightly with oil.
Bake until lightly toasted, about 7 minutes. Cool on baking sheet on a rack.
Spread each toast with 1 teaspoon fig jam and top with about 1 1/2 teaspoons goat cheese and 2 pieces fresh fig.
•Fig jam can be made 1 day ahead and chilled, covered. Bring to room temperature before using. •Toasts can be made 1 day ahead and cooled, then kept in an airtight container at room temperature.
