Whip 2 sticks butter on high in the bowl of a stand mixer using the whisk attachment. Switch to the paddle attachment. Add the raspberries. Turn the mixer to low for only about 5 seconds, just long enough for the berries to begin to mix in and break up, but not so long that it turns into a mess.
Turn the berry butter out onto a long sheet of plastic wrap set over a long sheet of foil. First seal the plastic wrap around the cylinder, and then secure the foil around it. Twist the ends, gradually applying more pressure as you twist in order to make the cylinder taut. Once it's a nice, neat cylinder of foil, place into the freezer for 30 minutes in order to quickly solidify it. Then transfer to the fridge until you're ready to use. The butter should be very firm.
Cut the bread into slices 1/2-inch thick. In a dish, whisk the egg yolks with the half-and-half, sugar, vanilla and lemon zest. Dip the bread slices in the egg mixture, coating both sides. Then remove from the dish and set aside. Repeat until all the bread is coated.
Heat a cast-iron skillet or griddle over medium heat. Sizzle some butter in the skillet when hot. Cook the French toast on both sides until golden brown, being careful not to burn. Remove the berry butter from the fridge. Unwrap one end and cut some slices. Lay one slice onto each serving of French toast. Sprinkle with powdered sugar if desired, and then drizzle with maple syrup.