This past spring I tried to find seed to grow some for a friend of mine and found that Broccolini is a registered trademark name for a cross between broccoli and a Chinese kale or Chinese broccoli, depending on whose story you read. Gai lan. Generic Broccolini goes as aspabroc. The name supposedly means the taste is described as a mix of asparagus and broccoli. I bought some seeds from Pinetree Seeds, grew 6 plants for my friend and 6 for me as I'd never messed with it before.
Here's my planting data in case that helps you decide if you have time to still do them:
Cell packs seeded Jan 11
Seeds up Jan 13
Transplanted to garden Feb 11
First cutting Mar 22
Since I have scratched that itch, the remaining seeds now live in the seed vault (freezer).