Bring the vegetable broth to boil in a medium sauce pan. Once boiling, whisk in the cornmeal in a slow steady stream, whisking constantly to prevent lumps. Continue whisking until the polenta begins to thicken (around 1 to 2 minutes). Add 1 teaspoon kosher salt.
Reduce the heat so that the polenta bubbles slowly. Continue to cook, stirring occasionally, for about 20 minutes until the cornmeal loses its raw flavor (taste every so often to check).
When the polenta is complete, turn off the heat and add the olive oil, and more kosher salt and pepper to taste. You can cover it to keep it warm before serving. If the polenta becomes too thick, you can stir in a bit of water to loosen it up.