Step 1In a medium-size, wide heavy-bottom saucepan, combine the butter, water, salt, sugar and vanilla seeds and bring to a rolling boil over high heat. Remove from heat and quickly stir in the flour (stir quickly or the flour lumps will cook). Return the pan to low heat and cook, stirring frequently, for about 3 minutes to cook the flour slightly and rid the mixture of any starchy, floury taste.
Step 2Remove the pan from the heat and place the dough in the bowl of a food processor or stand mixer. If using a food processor, process the dough for 15 seconds to cool slightly and release steam (leave the tube open), then add all of the eggs and egg whites at once. Immediately continue to process for 30 seconds to combine and form the cruller batter. If using a stand mixer, beat the dough with the paddle attachment until most of the steam has subsided, then add the eggs and egg whites, 1 at a time, until each is incorporated and a batter is formed.
Step 3Fill a deep fryer with oil, or fill a large pot to a depth of at least 3 inches, and heat to a temperature of 350 degrees.
Step 4Meanwhile, place the batter in a pastry bag fitted with a round tip no wider than 1/4-inch in diameter.
Step 5Bring the pastry bag over the hot oil and push the batter into the hot oil in a zig-zag or spiral shape. Fry no more than 1 large or 2 smaller funnel cakes at a time. Fry the cakes until puffed and golden (they will triple in size), 3 to 5 minutes, depending on size, and flipping every 30 seconds or so.
Step 6Drain the cakes on a rack and cool slightly, then top as desired.