Singular 'pea' is a backformation

The word pea was originally pease in the singular and peasen in the plural. Eventually, speakers understandably interpreted the -s in pease as the plural suffix rather than just a sound in the original Latin pisum/pisa and Greek πίσον, and the English singular pea was born.

For example, a 15th-century cookbook has the following recipe for what we would today call pea soup:

A fifteenth-century cookery-book. Harleian Collection 279. (~1420). Take grene pesyn, an washe hem clene an caste hem on a potte, an boyle hem tyl þey breste, an þanne take hem vppe of þe potte, an put hem with brothe yn a-noþer potte, and lete hem kele; þan draw hem þorw a straynowre in-to a fayre potte, an þan take oynonys, and screde hem in to or þre, an take hole wortys and boyle hem in fayre water: and take hem vppe, an ley hem on a fayre bord, an cytte on .iij. or iiij., an ley hem to þe oynonys in þe potte, to þe drawyd pesyn; an let hem boyle tyl þey ben tendyr; an þanne tak fayre oyle and frye hem, or ellys sum fresche broþe of sum maner fresche fysshe, an caste þer-to, an Safron, an salt a quantyte, and serue it forth.

Pease also functioned as a mass noun, like bread or oatmeal.

Pēse. Middle English Compendium. (2019). Yisterday I ete cale and pes, & to-day I eete pes & cale, & to-morn I mon eate pess with cale, & after to-morn I mon eate cale with pease.

Unfortunately, the above quote is taken from a religious anecdote promoting a moderate and uniform diet, and not a hilariously sarcastic comment by a medieval peasant.