10–12 medium jalapeños
1 tbsp. canola oil, plus more for frying
1/4 lb. lump crab meat, picked through
to remove any bits of shell
3 tbsp. cream cheese, at room temperature
1 tbsp. finely chopped cilantro leaves
1 tbsp. finely chopped parsley leaves
1 shallot, finely chopped
1 1/2 tbsp. plus 3/4 cup dried bread crumbs
2 tsp. fresh lime juice
1 egg yolk
1/2 cup all-purpose flour
1/2 cup milk
2 eggs, beaten
1 1/4 tsp. kosher salt, plus more to taste
1. Heat oven to broil; arrange a rack 6" from heating element. In a small bowl, toss jalapeños with 1 tbsp. oil. Transfer jalapeños to a foil-lined baking sheet; broil, turning several times, until blackened, about 12 minutes. Transfer jalapeños to a bowl, cover with plastic wrap, and set aside to let steam for 15 minutes. Peel the jalapeños. Working with 1 jalapeño at a time, cut a slit down the length of the pepper. Scoop out the seeds with a small spoon (handle carefully so that they stay intact). Set jalapeños aside.
2. With a fork, vigorously mix together crab, cream cheese, cilantro, parsley, shallots, 1 1/2 tbsp. bread crumbs, lime juice, and yolk in a bowl. Stuff each jalapeño with 1 heaping tbsp. of filling; transfer to a plate and repeat with remaining jalapeños. Refrigerate for 30 minutes.
3. Put remaining bread crumbs into a shallow dish. Put flour into another small dish. Whisk together milk and eggs in a bowl. Working with 1 jalapeño at a time, dredge jalapeño in flour, shaking off excess. Dip jalapeño in egg mixture, roll in bread crumbs, and transfer to a plate; set aside.
4. Pour oil to a depth of 2" into a 4-qt. saucepan over medium-high heat until a deep-fry thermometer reads 325˚. Working in batches, add jalapeños and cook, turning occasionally, until golden brown, about 3 minutes. Drain jalapeños on paper towels; sprinkle with salt.