Place the sheet of puff pastry on a non-stick surface and roll out until the seams are smooth. Cut the piece of puff pastry into 16 pieces.
Place 1 1/2 teaspoons of goat cheese onto each square of puff pastry.
Whisk together the egg and water to make an egg wash and lightly brush the egg mixture on the edges of each square. Make a packet with each square and place it on a sheet of parchment paper.
Heat the vegetable oil in a large dutch oven to 350℉. Fry the beignets in the oil for approximately 2 minutes. Remove and drain on paper towels.
To serve, place the beignets on a platter, drizzle with the honey, and top with the roughly chopped caramelized pecans.
In a nonstick skillet over medium-high heat, melt together the brown sugar and water until rapidly bubbling. Add the pecans, stirring thoroughly to coat. Cook, stirring, for 3-4 minutes, until fragrant and most of the liquid has evaporated. (But not so long at the sugars burn.)
Spread pecans into a single layer onto a parchment-lined baking sheet, and use a fork to separate them. Let stand at room temperature for about an hour, until fully cooled, set, and dry. (Pecans will be only very slightly tacky to the touch.)
Break apart any pecan clusters and store in an airtight container at room temperature for up to a week, in the refrigerator for a couple of weeks, or in the freezer for up to 2 months.
Serving Size 1