Prepare an ice bath by filling a large bowl halfway with ice cubes then filling it with cold water. Set aside.
Bring a large saucepan of water boil over high heat. Add the tablespoon of salt and the broccoli and blanch until a knife goes through easily, but a fork still meets some resistance, about 2-3 minutes.
Drain broccoli through a colander then submerge in the ice bath.
Once broccoli is cold, line a baking sheet with paper towels and place broccoli on the baking sheet and pat dry.
Heat olive oil in a large frying pan over medium-high heat. Add shallot and garlic and cook, stirring constantly until fragrant, about 1 minute. Add broccoli and cook, stirring, until broccoli is hot about 1-2 minutes more.
Taste and season with salt and pepper and serve.