Heat a large skillet over medium-high heat and add 1 tablespoon olive oil. When the oil is heated, add the broccoli, flat sides down, in an even layer, and sprinkle with 1/2 teaspoon salt. Let the broccoli cook undisturbed for 2 minutes. Flip the broccoli and continue cooking until the broccoli is tender-crisp, an additional 2 to 3 minutes. Remove the broccoli to a plate and set aside.
Turn the heat down to low and add 1/2 tablespoon olive oil. Add the garlic, shallot and chile flakes and cook, stirring frequently, until tender, 2 to 3 minutes. Turn off the heat and add the lemon zest and juice and stir to combine.
Spoon the lemon-shallot mixture over the broccoli and serve.