The elliptical baroque church at the end of Calle San José has a special place in Spanish history: it is where the Cortes of Cádiz met in 1812 to produce the first Spanish constitution — the "Pepa" as the constitution became known (it was signed on March 19th, San José's Day). The building's unusual oval plan and white interior were already complete when the parliament convened here, using the circular space and rising tiers of seating exactly as intended, though for political debate rather than religious ceremony.
Murillo's great painting of the Immaculate Conception hangs above the high altar, and several El Grecos are attributed to works in the collection. The church is open for guided visits and is small enough to see in 30 minutes. The Plaza de España just north of the old city has a monument to the 1812 constitution if you want to complete the historical circuit.