Place the whole potato in a small saucepan. Add enough cold water to cover the top of the potato and bring to a boil.
Once the water boils, reduce heat to medium low and cover. Cook the potato in lightly boiling water until tender, about 20 to 25 minutes.
Drain the water.
Once the potato is cool enough to touch, peel the skin off. It should come off easily.
Mash the potato in a food processor.
Remove the mashed potatoes, measure out 1 packed cup of them, and return it to the food processor. Use any leftover mashed potatoes however you wish.
Add salt, peanut butter, and brown sugar. Puree until fully combined.
Transfer to a bowl and knead in the sunflower seeds.
Divide the dough into two.
Roll each ball of dough out as thinly as you can (ideally just under 1/8”) on parchment or a silicone mat sized for a 9” x 13” cookie sheet. The dough tears easily, but you can patch holes by spreading the dough with your fingers. It may also help to roll the dough between two pieces of parchment. Don’t worry about making the dough a perfect shape, as these crackers will have a rustic look.
Transfer the rolled dough on the silicone mats or parchment papers to cookie sheets and refrigerate overnight to dry out.
Preheat oven to 350 F.
Sprinkle the rolled, chilled dough with coarse salt.
Bake for 20 minutes or until the edges of the crackers begin to look dark brown. Keep a close eye on the crackers as they can go from done to burnt very quickly.
Turn the sheets of crackers out onto a cooling rack.
When cool, break into snack-sized pieces.