Making a goats cheese tart more substantial
Eggs -- not enough to make it a quiche or custard, but enough to bind it together a bit, and give it a richer mouth-feel. I'd suggest either a single egg, or one egg + one egg yolk.

If you do decide on the potato, I'd cook it first -- cubed, tossed in olive oil with salt, pepper, and garlic, and roasted in a hot oven till brown. I'd use either Yukon gold or small waxy potatoes -- no russets; they're too mealy.