Begin by rinsing the broccolini under cold water to remove any dirt. Trim the ends of the stalks to ensure they cook evenly. If the stalks are particularly thick, you may want to slice them in half lengthwise.
Place your large skillet over medium heat. Add the 4 tablespoons of unsalted butter and let it melt, swirling the pan occasionally to prevent the butter from browning.
Once the butter has melted, add the 4 thinly sliced garlic cloves to the skillet. Sauté them for about 1-2 minutes until they become fragrant and start to turn golden. Be careful not to let them burn, as burnt garlic can impart a bitter taste.
Add the prepared broccolini to the skillet, tossing it gently to coat it in the garlicky butter. Sauté the broccolini for about 5-7 minutes, or until it becomes bright green and tender but still slightly crisp.
Remove the skillet from heat and squeeze in the lemon juice, starting with 1 tablespoon and adding more to taste. Season generously with coarse salt and pepper. Toss everything together until well combined.
Transfer the garlicky butter glazed broccolini to a serving dish. Enjoy it hot, garnished with a sprinkle of extra lemon juice or a zest of lemon for added brightness.