Preheat oven to 350°F In large bowl, beat butter with electric mixer for 30 seconds. Add brown sugar; beat until fluffy. Add one of the eggs; beat well. Slowly beat in 1 1/4 cups flour. Divide dough in half. Cover and chill one portion.
Spread remaining portion of dough onto bottom of 10 - inch spring form pan with side removed. Place pan bottom on baking sheet. Bake for 10 minutes; cool. Attach side of pan. Press chilled dough about 1 3/4 inches up side of pan.
Increase oven temperature to 450°F In bowl, combine cream cheese and 1 1/4 cups granulated sugar; beat until fluffy. Beat in 1/4 cup flour until smooth. Add remaining eggs and 1 tablespoon vanilla; beat on low speed just until combined. Stir in 1/2 cup of the sour cream. Pour into pan. Place in shallow baking pan. Bake for 10 minutes.
Reduce oven temperature to 300°F Bake for about 30 minutes or until center appears nearly set when gently shaken. Remove from oven. In small bowl, combine remaining sour cream, 1/4 cup granulated sugar, and 1 teaspoon vanilla; spread over cheesecake. Bake for 15 minutes more.
Cool on wire rack for 15 minutes. Loosen crust; cool for 30 minutes. Remove side of pan; cool cheesecake. Cover and chill for 4 to 24 hours. Let stand at room temperature for 15 minutes before serving.