If you want to bake parakeets into a pie you should refer to the 1598 Italian cookbook, Epulario or the Italian Banquet. Back in those times hosting a banquet was no small task. In addition to providing delicious and exquisite food for your guests, you were also supposed to entertain with theatrics, often using the food as a prop.
One such theatric is documented in the poem Sing a Song of Sixpence. Remember that nursery rhyme?
Sing a song of sixpence,
A pocket full of rye,
Four and twenty blackbirds
Baked in a pie.
When the pie was opened
The birds began to sing—
Wasn’t that a dainty dish
To set before the king?
Putting live birds in a pie and then cutting it open to create a fluttering marvel was just one of the many strange ways hosts had to “keep up with the Jones” back then. Below is a recipe that these hosts of yore may have referenced (or probably their kitchen staff). It calls for 3 parakeets or 6 finches. Notice that the last line instructs the host to offer real dessert for the guests in addition to the performance dessert so they don’t feel made fun of.
Make the coffin of a great Pie or pasty. in the bottome whereof make a hole as big as your fist, or bigger if you will. let the sides of the coffin be some what higher then ordinary Pie, which dome. put is full of flower and bake it, and being baked, open the hole in the bottome and take out the flower [flour]. then having a Pie of the bignesse of the hole in the bottome of the coffin aforesaid. you shal put it into the coffin, withall put into the said coffin round about the aforesaid pie as many small live birds as the empty coffin will hold besides the pie aforesaid. And this is to be done at such time as you send the Pie to the table, and set before the guests: where uncovering or cutting up the lid of the great Pie, all the Birds will flie out. which is to the delight and pleasure shew to the company and because they shall not bee altogether mocked, you shall cut open the small pie and in this sort tart you may make many others, the like you may do with a Tart.