In a large pot of salted boiling water, boil Brussels sprouts until bright green and fork-tender, 8 to 10 minutes. Drain and rinse with cold water.
Arrange egg and flour in two shallow bowls and place panko bread crumbs in a large Ziploc.
Dredge Brussels sprouts: Dip in egg, then toss in flour, then add to panko bag. Shake in batches until fully coated.
Meanwhile, fill a skillet with enough canola oil to reach 2″ high and heat over medium-high heat until shiny. Add dredged Brussels sprout to oil and fry until golden and crispy, 3 to 4 minutes. Transfer to a paper towel-lined plate and season with salt and pepper.