Preheat oven to 425°F. Line a baking sheet with parchment paper.
Spread broccoli and asparagus on the prepared baking sheet. Drizzle with 2 tablespoons olive oil, sprinkle with lemon pepper and salt, and toss to coat. Nestle the lemon halves cut-side down on the baking sheet.
Roast for 15-18 minutes, stirring once halfway through, until the vegetables are tender-crisp and lightly charred, and the lemon is caramelized.
Heat ½ cup vegetable oil in a small skillet over medium heat. Add shallot rings, shaking off excess cornstarch and fry in the oil. Stir often, and fry until golden brown and crispy, about 4-5 minutes. You may need to fry them in batches, depending on the size of your pan. Transfer to a paper towel–lined plate and sprinkle with a pinch of salt immediately when they are removed from oil.
When the broccoli and asparagus are done, drizzle with the remaining tablespoon of olive oil. Squeeze the roasted lemon halves over the vegetables and toss gently.
Transfer to a serving platter, sprinkle with crispy shallots, and enjoy!