Heat oil in a large cast iron skillet (or other large, durable skillet) over medium high heat. You can tell that the oil is hot enough if you throw a pinch of flour into it and it sizzles. If it starts to smoke in any way, remove from heat immediately.
In one bowl, whisk together egg and milk. In another larger bowl, combine flour,baking powder, and salt. Pour wet mixture over dry mixture and stir until it just comes together. Gently fold in corn and peas.
Once oil is hot enough, gently drop heaping tablespoons of the fritter batter into the pan, leaving a few inches in between each fritter. Press down gently with the back of a wooden spoon or spatula to flatten slightly.
Fry until golden brown (approx 45 seconds) then flip once and brown on the other side (approx another 45 seconds). Carefully remove with spatula to drain on a paper towel lined cooling rack.