Crust
Preheat oven to 375degrees (I used 365degrees in my Thermador Convection oven)
Combine the melted butter, sugar and vanilla in a small bowl then add the flour and salt and blend. The dough is soft. Press the dough into the bottom and sides of a 9 inch tart pan with a removable bottom.
Bake the crust in the oven for 18 minutes or until brown. I baked mine for 16 minutes and even with the heat reduced my convection over-browned a bit. Place the crust on a rack and allow to cool.
Filling
Whisk eggs, sugar, salt in a medium sized bowl until blended.
Place diced butter in a small, heavy saucepan with a light color bottom so you can watch the butter as it cooks. I used an old white Pyrex sauce pan. Heat the butter over medium heat, stirring frequently for about 6 minutes until it begins to get brown flecks. Don't let the butter burn! This is not a good time to answer the phone.. stay with the butter until it is brown. Pour the browned butter into a glass measuring cup.
Whisk a small amount of the butter into the egg mixture to temper then slowing add the rest of the butter until it is well incorporated.
Place the fresh raspberries in the crust with narrow-ends up.
Now pour the mixture over the raspberries
Bake for about 40 minutes. Mine baked in about 30 at a reduced temperature.
Once the tart is cooled, remove it from the pan and place on a platter. This tart can be baked ahead (if you are a planner.. ) otherwise its a relatively quick, wonderful dessert.