In the bowl of a stand mixer fitted with the dough hook, combine the flour, yeast, and sugar. Mix on low speed for 1 minute to blend. With the mixer running, slowly pour in the canola oil and lukewarm water. Once the dough begins to come together, add the salt. Increase the speed to medium-low and knead for at least 10 minutes, until the dough is smooth and elastic. If kneading by hand, use a large mixing bowl and work the dough on a floured surface until it passes the windowpane test.

Transfer the dough to a large greased mixing bowl, cover with plastic wrap or a clean kitchen towel, and let rise at room temperature until doubled in volume, about 1 hour.

Heat the olive oil in a wide skillet over medium-low heat. Add the onions and a pinch of salt. Cook, stirring often, for 25 to 30 minutes, until the onions are soft, deeply golden, and fragrant. Reduce the heat if they begin to brown too quickly. Remove from the heat and let cool.

Preheat the oven to 350°F (175°C), using the convection setting if available.

Punch down the dough to deflate it and transfer to a clean work surface. Divide into 2 or 3 equal portions. For each loaf, divide the dough into 4 equal strands and braid into a four braided challah. For added flavor, gently fold some of the caramelized onions into the dough before shaping, or reserve them for topping.

Place the shaped loaves on a parchment-lined sheet pan. Cover loosely and let rise again for 30 minutes, until slightly puffed.

Brush the loaves evenly with the beaten egg. Top with poppy seeds, onion flakes, and caramelized onions, pressing gently so the toppings adhere. Bake for 25 to 30 minutes, until the challahs are deep golden brown. Check the bottom—when tapped, it should sound hollow and appear golden, not pale.

Cool on a wire rack for at least 30 minutes. Sprinkle with flake sea salt and parsley.