In a large pot fitted with a steamer basket, bring about 1/2 inch of water to boil over high heat. Add the Broccolini, cover, and steam until just tender, 6 to 7 minutes. Transfer to a large towel-lined baking sheet and let cool briefly; then pat very dry with another towel.

In a 12-inch skillet, cook the bacon over medium heat, stirring frequently, until golden, about 5 minutes. Use a slotted spoon to transfer the bacon to a small bowl, leaving the fat in the pan.

Increase the heat to medium high and arrange half of the Broccolini in a snug single layer in the skillet, making sure all have good contact with the bottom of the pan. Sprinkle with 1/4 tsp. salt. Let cook undisturbed until browned in spots, about 1-1/2 minutes. Transfer to a serving platter. Add 1 Tbs. of the olive oil to the skillet and sear the remaining Broccolini, sprinkling it with another 1/4 tsp. salt.

Return the first batch of Broccolini to the skillet. Sprinkle with the bacon, lemon juice, chile, and the remaining 1 Tbs. of olive oil. Toss well to combine and remove from the heat. Sprinkle with the Parmigiano, quickly toss to combine, and transfer to the serving platter. Serve immediately.