Position a rack in the bottom-center of your oven and preheat to 350º. Line a 9 x 9" square pan with 2 pieces of parchment paper or aluminum foil cut to fit width-wise, leaving an overhang on each side. (This will help you lift the cake out of the pan after baking, making cutting easier.)
Spread the pistachios on a small baking sheet and toast lightly, about 8 minutes, until light golden and fragrant. Let cool completely. Combine the cooled nuts in a food processor with the flour, sugar and salt. Add the butter and pulse until the mixture begins to form large, coarse crumbs, and holds together when squeezed, about 30 pulses. Dump the mixture into the lined pan, and press firmly and evenly with your fingers.
Bake the crust until golden and firm, about 30 minutes. Let cool slightly, at least 10 minutes.
Wipe out the food processor. Combine the cheeses, sugar, vanilla bean seeds, lemon zest and salt and blend until smooth, about 5-10 seconds. Add the flour and process until smooth, another few seconds. Add the eggs, process until smooth, then scrape down the bowl. Add the cream and process until smooth. Scrape once more, and blend again if at all lumpy.
Scatter the berries evenly over the cooled crust. Pour the filling over. Bake the cheesecake until the center is set,30 - 40 minutes. It should wobble like jell-o when you shake it gently, but not be watery or liquid. Remove to a cooling rack and let cool 1 hour, then cover with plastic wrap and chill for at least 3 hours, or overnight, until firm and cold.
To slice the bars, loosen the sides and bottom with a small, offset spatula. Carefully lift out of the pan (it may crack a little bit, but this is not the end of the world.) Place on a large cutting board. Fill a pitcher with hot tap water and have some paper towels handy, or an old (but clean!) dish towel that you don't mind getting stained. Dip a large chef's knife in the hot water and wipe completely dry between cuts. I cut mine 4 by 4 for sixteen 2" squares; you can then cut these on the diagonal for 32 triangles. Or cut the bars 8 by 8 for 64 bite-sized cubes.
Store in an airtight container in the fridge for up to four or five days.
Adapted from Williams Sonoma Baking.A heads up on timing: these bars take about 1 1/2 hours total to assemble and bake, plus an additional 4 hours to cool and chill. They are excellent the day of and after baking, when the crust is still crisp, but keep well for up to 4 or 5 days in the fridge.To quickly warm your cheeses and eggs to room temperature (essential to achieving non-lumpy cheesecake), place a towel on top of your preheating oven. Scoop the cheeses into a metal bowl, and the eggs (cracked or not) in another bowl. Place the bowls on the towel while you make your crust. Rotate occasionally, and remove when they reach room temperature to the touch.The bars are easily made in a food processor. Lacking one, you can chop the nuts finely by hand, and mix both the crust and filling in a stand mixer with the paddle attachment, or by hand in a large bowl.For a more pronounced goat cheesy flavor, substitute another 2 - 4 ounces of chevre for an equal amount of cream cheese.For thinner bars, you could bake the cake in a 9 x 12" rimmed (quarter) sheet pan, baking time adjusted.Nutritional values are based on one of sixteen bars.