In the bowl of a food processor combine the sun-dried tomatoes, sunflower seeds, basil leaves, Parmesan, 3 smashed garlic cloves, and lemon juice. Add half of the olive oil and puree until smooth. If the mixture seems too thick add more olive oil. Taste and adjust seasoning with salt and pepper. Remove it from the food processor, pour it into a bowl and refrigerate if not using immediately.
Put the baguette slices onto a baking sheet in 1 layer and toast them on both sides under the broiler until golden brown. Remove them from the broiler and rub each slice with the whole garlic cloves.
Spread the toasts with the softened goat cheese, top each with a teaspoonful of sun-dried tomato pesto, and garnish with the remaining basil that has been cut into chiffonade. Arrange on serving platters and serve.