Add the chives, dill, parsley, thyme, salt and cayenne to the cooled mixture and stir well. Stir in the egg and half each of the bread crumbs and almonds. Gently fold in the crabmeat; the mixture should be lumpy.
On a plate, stir together the remaining bread crumbs and almonds. Have ready a baking sheet. With clean hands, divide the crab mixture into 12 equal portions, then shape each portion into a cake the diameter of an English muffin. As you form each cake, gently press both sides of it into the crumb-almond mixture to coat well, then place on the baking sheet. When all of the cakes are ready, cover the pan loosely with plastic wrap and refrigerate for at least 1 hour or up to 3 hours.
To cook and serve the crab cakes: Preheat the oven to 200 degrees. Have ready a large baking dish. In a large skillet, combine 2 tablespoons of the butter and 2 tablespoons vegetable oil over medium-high heat. When the butter is melted, add half of the crab cakes and sauté, carefully turning them once with a spatula, until they are golden brown on both sides and cooked through, about 4 minutes on each side. Transfer to the baking dish and keep warm in the oven while you cook the remaining crab cakes the same way, adding more oil to the pan if needed to prevent sticking.
When the crab cakes are almost done cooking, toast the English muffins and spread them lightly with a little of the remaining butter. Place 1 or 2 muffin halves, cut side up, on each individual serving plate, or place them all on 1 or 2 large platters.
To cook the eggs and serve: As soon as all of the crab cakes are cooked and in the oven, wipe out the skillet, return it to medium-high heat, and melt enough of the remaining butter in it to coat the bottom evenly when you swirl the pan. Carefully crack just enough eggs into the pan to fit without crowding and sprinkle them with salt. Fry until the whites are set and the yolks are cooked to your or your guest's liking, spooning a little of the butter from the pan over the whites and yolks to help them set, 3 to 5 minutes.
Transfer the same number of crab cakes to muffin halves as eggs you cooked, and top each crab cake with a fried egg. Repeat with the remaining butter, eggs, and crab cakes. Garnish the eggs with the chives and serve right away.