Red Velvet Swirl Brownies

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1 tablespoon unsalted butter, for pan

Red Velvet Brownie Layer:

1 stick unsalted butter

1 cup sugar

1 teaspoon vanilla extract

1/4 cup cocoa powder

Pinch salt

1 tablespoon red food coloring

1 teaspoon vinegar

2 eggs

3/4 cup all-purpose flour

1/4 cup chopped toasted walnuts

Cream Cheese Layer:

8 ounces cream cheese, softened

1/4 cup sugar

1 egg

1/8 teaspoon vanilla extract