Preheat oven to 375°F. Position a rack in the center. Use ungreased cookie sheets or line them with parchment paper if you prefer.
In a large bowl, beat 3/4 cup (1-1/2 sticks) softened butter, 3/4 cup granulated sugar, and 3/4 cup packed light brown sugar until well blended and creamy.
Add 2 eggs and 1 1/2 teaspoons vanilla extract; beat until fully incorporated.
In a separate bowl, whisk together 1-1/4 cups all-purpose flour, 1 teaspoon baking soda, 1 teaspoon ground cinnamon, and 1/2 teaspoon salt.
Gradually add the dry mixture to the butter mixture, mixing until just combined and no dry streaks remain. Do not overmix.
Stir in 3 cups quick-cooking oats and 2 cups butterscotch chips until evenly distributed.
Drop dough by heaping teaspoons onto the ungreased cookie sheet, spacing cookies about 2 inches apart to allow for spreading.
Bake 8 to 10 minutes, or until the edges are set and cookies are golden brown.
Remove from oven and let cookies cool on the cookie sheet for about 2 minutes, then transfer to a wire rack to cool completely.
Makes about 4 dozen cookies.