Preheat the oven's broiler and set the oven rack about 6 inches from the heat source.
Heat great northern beans with about 1/4 cup of liquid in a saucepan over low heat; stir in thyme, Gorgonzola cheese, sun-dried tomatoes, black pepper, and 1 clove minced garlic. Heat gently to melt Gorgonzola; keep bean mixture warm.
Arrange slices of baguette on a baking sheet and toast under the broiler, about 1 minute; watch carefully. Remove bread slices and rub each slice with a garlic clove half. Spread each slice with goat cheese and top with a basil leaf. Spoon bean mixture onto the appetizer and serve warm.