Split the vanilla bean lengthwise and scrape out the seeds.

Combine the type 45 wheat flour, fresh baker's yeast, salt, whole milk, eggs, and vanilla seeds in a mixing bowl.

Mix on low speed until the dough becomes smooth and homogeneous.

Add the cold unsalted butter gradually, adding one piece at a time while mixing.

Add the brown sugar and knead until it is fully incorporated into the dough.

Knead the dough for a few minutes on second speed until elastic. Scrape the dough from the bowl as needed.

Shape the dough into a rough ball and place it in the mixing bowl.

Cover the bowl and let the dough rise at room temperature for 60 min, until visibly puffed.

Deflate the dough gently and cover it directly against the dough surface with plastic wrap.

Refrigerate the covered dough overnight for about 12 hours.

Roll the chilled dough to about 1 cm thick on a lightly floured work surface.

Cut the dough into 12 round beignets and transfer them to greased parchment-lined baking sheets.

Cover the shaped beignets and let them proof at room temperature for 60 min, until light and airy.

Heat the neutral frying oil in a deep saucepan to 170°C (340°F).

Fry the beignets in small batches for 2 to 3 min per side until deep golden brown.

Lift the fried beignets from the oil and drain them on a wire rack.

Toast the pistachios gently in a dry saucepan until fragrant, without browning them too deeply.

Cool the toasted pistachios completely before making the praline.

Melt the granulated sugar in a clean dry saucepan until it forms an amber dry caramel.

Reserve about one-third of the caramel for the praline and keep the remaining caramel warm for coating.

Blend the cooled pistachios with the reserved caramel until a thick paste forms.

Add the neutral oil only if needed and blend until the pistachio praline is smooth enough to pipe.

Transfer the pistachio praline to a piping bag and fill each cooled beignet from the side.

Dip or drizzle the filled beignets with the remaining caramel. Let the caramel set before serving.