Preheat oven to 335°F / 170°C and line a 9-inch square cake pan with parchment paper.
In a large bowl, whip together the eggs and sugar with a whisk until light and thick, like custard. This should take about 30 seconds of vigorous hand whisking.
Put the chocolate and butter in a heat-proof bowl and microwave in 30-second intervals until completely melted. Make sure you give it a little stir in between blasts.
Pour the melted chocolate mixture into the egg/sugar mixture and whisk together lightly, just until combined.
Add the vanilla and almond extract and mix in.
Fold in the flour and salt until just combined.
Add the chopped pistachios and mix until evenly distributed.
Pour the brownie batter into the prepared cake pan and spread out into an even layer.
Bake for 20-25 minutes. The top should be shiny and crinkly, and a skewer inserted will come out slightly gooey.
Remove from the oven and leave the brownies in the pan to cool completely.
Make the Pistachio Ganache
While the brownies are baking, you can make the ganache as it will need to cool before you can use it.
Chop up the white chocolate into small pieces that will melt easily and place in a heatproof bowl.
Pour the heavy cream into a saucepan over medium-low heat. Let it warm up just until it is scalding (tiny little bubbles just start to appear on the surface). Remove from the heat and pour over the chopped chocolate. Let sit for 1 minute.
Stir the hot cream and chocolate together until the chocolate has completely melted - it should make a smooth, shiny ganache.
Add the pistachio paste and salt and mix until combined.
Check the flavor of the ganache, if you would like to you can add a few drops of almond extract punch up the flavor a little.
Let the ganache cool to room temperature before spreading over the cooled brownies.
Notes
It's always best to measure your ingredients with a kitchen scale, rather than with cup measures. It's incredibly hard to measure dry ingredients accurately with cups, and in a recipe like this, having the wrong ratios of ingredients could really mess up the final result. I always provide my recipes in both cups and grams so you can choose what works best for you, but if you are using cups please be aware of the lack of accuracy and how it could impact your bakes.