Start by activating the yeast for the beignet dough. Pour the warm milk into a small bowl or glass measuring cup. Add 1 tbsp (12g) of the granulated sugar and sprinkle the yeast overtop. Stir and allow to sit for 5-7 minutes, until frothy and activated.
In a large bowl, whisk together the flour and salt. Set aside.
Once activated, pour the yeast mixture into the bowl of a stand mixer (or a large bowl if mixing/kneading the dough by hand). Add the rest of the sugar (½ cup minus the 1 tbsp that was used to activate the yeast), eggs, butter, vanilla, and the flour mixture.
With the dough hook attachment (or with a wooden spoon if mixing by hand), mix on low speed for 1 minute, until barely combined. Allow to rest for 5 minutes so the flour can soak up the liquids.
Then, mix on medium speed for 7-8 minutes, until the dough is elastic, smooth, and is pulling away from the sides of the bowl. If the dough seems a little too sticky, you can add 1 tbsp more flour at a time, until it starts to pull away from the sides of the bowl.
Transfer the dough to a lightly oiled bowl. Cover and allow to rise in a warm environment for 1-1.5 hours, or until doubled in size.
Once the dough is almost finished rising, cut out 16 squares of parchment paper and spread them across 2 baking sheets.
Once the dough is doubled, punch it down and turn it onto a lightly floured surface. Roll the dough out to a 10x10” square that ~½” in thickness. Using a pizza cutter or knife, cut the dough into 16 squares.
Place the beignets onto the prepared parchment paper squares on the baking sheets. Loosely cover with a kitchen towel and allow to proof for 30-45 minutes, until puffy.
While the beignets are proofing, prepare the french hot chocolate. In a medium saucepan over medium heat, add the milk, heavy cream, sugar, cocoa powder, and instant coffee (if using). Stir to combine and heat until heated through. Add the chocolate and whisk until the chocolate is fully melted. Then, remove from the heat and whisk in the vanilla and salt.
Once the beignets are almost done proofing, fill a large, heavy-bottomed pot or Dutch oven with oil, filling ~2” in the pan. Heat on medium-high until it reaches 350F-365F.
Line a wire cooling rack with a thick layer of paper towels.
Once the oil is hot enough, carefully transfer the parchment paper squares with the beignets on them slowly into the hot oil, 3-4 at a time. Fry the beignets for 1-2 minutes on each side (2-4 minutes total), until a golden brown.
Using a slotted spoon, carefully remove the beignets from the oil and transfer to the rack with paper towels. Repeat with the remaining beignets.
Once ready to serve, prepare the whipped cream (if using). Add the heavy whipping cream, powdered sugar and vanilla extract to the bowl of a stand mixer (or mixing bowl). Use the whisk attachment or a hand-held mixer, and beat the ingredients together until stiff peaks form.
Gently reheat the hot chocolate over the stove (if needed). Serve the beignets warm with a generous dusting of powdered sugar and a cup of the hot chocolate with the whipped cream.
