You will need to make your polenta crust at least 2 hours in advance, so that it has adequate time to chill. In my case, I made it the night before to make assembly time of about 10 minutes the next day. Place your water, olive oil, salt, and dry basil into a medium saucepan and bring to a boil over medium-high heat. Once boiling, slowly pour your polenta into the pot while continuously whisking to prevent unpleasant clumping. Once combined, turn your heat down to low and continue to cook while stirring every few minutes until the mixture becomes thick. This will take about 15 minutes. Remove from the heat and stir in your parmesan cheese.
Lightly coat a jelly roll pan or a cookie sheet with oil. Pour the polenta on the pan and spread it out in a roundish shape that is large enough to cut your pie crust out of, but not so large that you end up wasting a ton of polenta. Allow it to cool for about an hour and then chill it for at least 1 hour before assembling your heirloom pie.
After the polenta has chilled, find something round whether it be a bowl or a cake tin, to use as a guide for cutting out your round pie shape. Place it on top of the polenta and cut around the edges with a knife as if you're tracing. Transfer it to whatever plate or cake stand you plan to serve it on.
Spread a layer of farmer's cheese over the polenta and then drizzle with balsamic vinegar and olive oil.
Cut your heirlooms into 1/4 inch slices and arrange them however you wish over your pie. Season with salt and pepper to taste before serving.