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Using a food processor or immersion blender, blend burrata and lemon zest for only 20-30 seconds until fluffy and whipped. Set aside.
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Grill steak to your liking. Remove from grill, tent with foil and let rest while preparing romaine.
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Brush the cut sides of the romaine with olive oil, then sprinkle with salt and pepper.
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Grill the romaine, cut-side down, until lightly charred but not overly wilted, 2 to 3 minutes. Carefully flip and grill for 1 or 2 more minutes.
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Transfer romaine wedges to a platter.
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Slice the steak and place on romaine.
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Drizzle basil oil over the steak.
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Scatter dollops of burrata on the lettuce.
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Serve immediately while still warm.