Heat oven to 350 degrees. Line 2 large baking sheets with parchment paper.
Whisk the flour, baking soda and salt in a small bowl. Mix the butter and both sugars in a large bowl with a wooden spoon until creamy. Beat in the egg until incorporated, then stir in the cream and vanilla.
Add the flour mixture and gently stir until no traces of flour remain. Add the oats, chocolate chips and nuts (if using), and fold until evenly distributed. Loosely scoop a rounded ball of dough using a measuring tablespoon or small cookie scoop and drop onto a prepared sheet. Repeat with the remaining dough, spacing the balls 2 inches apart.
Bake, 1 sheet at a time, until golden brown, 12 to 14 minutes. Cool on the sheet on a wire rack for 1 minute, then transfer the cookies to the rack to cool completely. The cookies will keep in an airtight container at room temperature for up to 5 days or in the freezer for up to 2 months.
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