Preheat an oven to 375°F/190°C. Lightly oil a baking dish just large enough to hold the dates in a single layer.
In a small fry pan over medium heat, warm the olive oil. Add the bread crumbs and cook, stirring constantly, until the bread crumbs are evenly golden brown, about 1 1/2 minutes. Remove the pan from the heat, transfer the bread crumbs to a plate and let cool.
Using a small knife, make a small lengthwise incision in each date. Carefully remove the pits. Stuff 1 tsp. of the goat cheese into the cavity left by each date's pit. Arrange the dates, with the goat cheese side facing up, in the prepared dish. Sprinkle the bread crumbs evenly over the top. (The dates can be prepared up to this point up to 24 hours in advance. Store, tightly covered, in the refrigerator.)
Bake the dates until warmed through, 10 to 12 minutes. Transfer to a serving platter and serve warm.