Preheat oven to 350 degrees F. Grease and line an 8-inch square pan with parchment paper so that the paper hangs over the sides.
In a food processor, pulse artichokes, spinach, onion, garlic and oregano, if using, until finely chopped but not puréed. Pulse in eggs, then pulse in breadcrumbs and Asiago. Scrape mixture into prepared pan, spread to level and bake for 20 to 25 minutes until set. Cool to room temperature before slicing into squares and store refrigerated.
Square can be served at room temperature or warmed in a 325 degrees F for 10 minutes.