Fitch calls himself an experimental historian. He makes the foods described in the cookbooks of yore; his site is called Cooking the Books.

The specimen above is called a cockentrice (or cockentryce). It is, quite literally, a pig's upper body sewn onto a turkey bottom. The recipe for it dates from the 15th-century, although it was known to be made in later years. Here's how one source describes what to do (a capon, FYI, is just a big chicken):

Cockentrice - take a capon, scald it, drain it clean, then cut it in half at the waist; take a pig, scald it, drain it as the capon, and also cut it in half at the at the waist; take needle and thread and sew the front part of the capon to the back part of the pig; and the front part of the pig to the back part of the capon, and then stuff it as you would stuff a pig; put it on a spit, and roast it: and when it is done, gild it on the outside with egg yolks, ginger, saffron, and parsley juice; and then serve it forth for a royal meat.

Fitch, true to the recipe, also created the poultry head-pig behind combination, too. Here it is roasting on a spit:

There is a variation on this dish called the Helmeted Cock in which the bird is made to ride the pig in military regalia.

These dishes are not even the most technically complex dish that was served to the royals of the era. During long meals, certain dishes called subtleties (or entremets) were often presented. The dishes themselves were supposed to be entertaining, and they sometimes included actual entertainment.

One dish, Rôti Sans Pareil, must be considered the direct ancestor of the modern turducken, though it bears the sort of relationship that Methuselah would have with modern centenarians.

Because the "Roast Without Equal" was formed by stuffing 17 birds inside each other like Russian dolls! Seventeen engastrated birds! In order, they were:

Warbler

Bunting

Lark

Thrush

Quail

Lapwing

Plover

Partridge

Woodcock

Teal

Guinea Fowl

Duck

Chicken

Pheasant

Goose

Turkey

Giant Bustard

(Note that our modern variants swap the duck and chicken positions.)

Now, it is fair to ask why such dishes would be made.

First, why these specific creatures: why the chimeras? There are many answers, I'm sure. The European discovery of the Americas with their many strange new animals might have made anything seem possible. The Renaissance-inflected desire to look back to the Classical civilization with its many animal (and human-animal) hybrids might have made such combinations seem more clever, too.

And the scholars Miguel de Asua and Roger French note that Europeans connected the Classical literature to the American animals easily.

Their strange forms were displayed in drawings and paintings as symbols of all that was exotic and alien, wild and fearsome. They were compared and identified with the fantastic beasts about which the Classics had talked, they were viewed as living 'jigsaw puzzles' composed of parts of other animals.

Living jigsaw puzzles.