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Preheat oven to 375 degrees.
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Mix butter and sugars until light and fluffy, a couple minutes (I used a stand mixer).
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Blend peanut butter into mixture.
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Add vanilla and eggs; mix until well combined.
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In a separate bowl, whisk together flour, baking soda, and salt.
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Add flour to peanut butter mixture and mix well.
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Mix M&M's® into dough by hand.
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To form cookies, scoop 1/3 cup dough and roll it into a ball.
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Place dough on cookie sheet and flatten (they should be somewhere between 1/4 to 1/2-inch thick).
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Bake cookies for about 12 minutes or until golden brown on bottom.
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Remove cookies from oven, then let cool on pan for 5 minutes. (If desired, decorate cookies with additional M&M's® as soon as you remove cookies from oven.)
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Transfer cookies to a wire rack and let cool completely before proceeding.
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Cover bottom side of cookie with 1/3 cup ice cream.
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Top with another cookie.
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Repeat with remaining cookies, then freeze ice cream sandwiches until solid, about 2 hours.
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Once frozen, serve ice cream sandwiches immediately or wrap in plastic wrap or parchment paper to save for later. Enjoy!