Preheat the oven to 350°F and line baking sheets with parchment paper.
Melt the butter in a medium saucepan over medium heat. Continue cooking until the butter is fragrant and lightly browned, stirring frequently. Remove from the heat and let it cool slightly.
In a large bowl, whisk together the flour, baking soda, and salt.
In a separate bowl, whisk the cooled butter, brown sugar, granulated sugar, egg, and vanilla until smooth and well combined.
Add the wet mixture to the dry ingredients and stir with a spatula until a soft cookie dough forms.
Gently fold in the crispy rice cereal, miniature marshmallows, and toffee bits, taking care not to crush the cereal.
Scoop the dough into portions and place them several inches apart on the prepared baking sheets.
Bake for about 10 minutes per batch, or until the cookies are lightly golden around the edges and still slightly soft in the centers.
Immediately sprinkle the warm cookies with a little flaky sea salt, if desired.
Let the cookies cool on the baking sheet for several minutes before transferring them to a wire rack to cool completely.