Set an oven rack in the middle position. Preheat the oven to 375 degrees F. Line a baking sheet with parchment paper or a silicone mat.
In a medium mixing bowl, drizzle 2 tablespoons of olive oil over broccolini and sprinkle with salt and black pepper. Toss to coat. Arrange the broccolini in a single layer on the prepared sheet tray. Bake in the oven for 10 to 15 minutes until tender and lightly browned. Remove from the oven and set aside to cool completely.
Lay crescent rolls on the counter and divide into the precut triangles. Lay a half slice of cheese on the wide part of the dough, squirt or spread about 1/2 teaspoon of mustard, then roll each dough around a broccolini stem to just below the floret. It’s ok if the cheese peeks out a little, it will just be crunchy cheese bits.
Place the rolls on the prepared baking sheet, evenly spaced apart. Beat the egg with a little bit of water, then brush on each roll. Sprinkle with poppy seeds and flaky salt. Bake for 20 minutes or until the crescent is golden brown and puffed and the broccolini edges are browned. Eat immediately or you can keep them in the fridge for a snack. Serve with ranch dressing, for dipping.
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