Stir together the butter, basil, shallot and lemon juice in a medium bowl using a rubber spatula; season with 1/4 teaspoon salt and a few grinds of pepper. Serve at room temperature or transfer the butter to a piece of plastic wrap, wax paper or parchment and roll it up, twisting the ends to make a tight log. Refrigerate for 1 week or freeze for up to 1 month.
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