In a large bowl of a stand mixer, combine the starter and all of the panini ingredients.
Mix on low speed or with a wooden spoon until the dough comes together. The dough should be very soft and slightly sticky.
If needed, add a little more flour. Knead for 5 minutes, or until the dough becomes smooth and elastic.
Cover and let rise for one hour, or until doubled in size.
Heat the oven to 350 F.
Shape the dough into 10 balls ( about 5 ¼ ounces each). *** See Note down below.
Flatten each panini with the palm of your hand until they measure about 4 inches across.
Place the panini on a baking sheet, cover with a cloth and let rise until puffy, about 45 minutes.
Sprinkle the tops of the panini lightly with flour.
With a sharp knife, score two lines in the top of each.
Bake for 20 to 30 minutes, or until golden brown on the top and bottom.
Cool on a wire rack.