In a medium saucepan, cook butter until it browns, about 5-8 minutes. The butter will foam. Stir often and scrape into a large bowl to cool slightly.
In a separate bowl, add flour, baking soda, and salt. Whisk and set aside.
Leave brown butter to cool for 10 minutes. Add brown sugar and sugar. With an electric hand mixer, beat on medium speed until the sugars and butter have combined, about 1-2 minutes.
Add the vanilla and the eggs, one at a time. Beat on low speed until combined and then switch to medium speed. The mixture will turn lighter in color and begin to thicken. This happens very quickly and should take about 30-60 seconds minutes.
Add flour and mix on low until just combined.
Switch to a hand-held spatula and add chocolate chips and toffee bits. Mix until fully combined.
Set aside for 30 minutes. The batter will thicken a little.
Meanwhile, preheat the oven to 375F/190C and line sheet pans with parchment paper.
Using a small ice cream scoop, drop heaping spoonfuls of cookie dough onto the sheet pan. About 1 heaping Tbsp per cookie. Do not flatten as the cookies will spread on their own. Sprinkle with flaky sea salt.
Bake until edges are golden brown and firm but the center is still soft, anywhere from 7-11 minutes. The cookies will be puffy when they first come out of the oven but will "collapse" as they cool. Let cool on the baking sheet for 10 minutes before transferring to a wire rack.
*1 Although it will be tempting to use a small sauce pan to melt the butter, use a medium size one. The greater surface area will allow the butter to brown faster. Also, I recommend a non-teflon coated one (i.e., stainless steel, etc.) as the teflon coating interferes with browning the butter.
*3 UPDATE: Cool the browned butter for 10 minutes so the eggs are not tempered (partially cooked) when you add them to the hot butter. Also, make sure NOT to use a stainless steel bowl, as they keep their heat very easily. I recommend using a bowl made with ceramic, glass, or bamboo.
*7 Parchment paper is the key to easy removal of the cookies from the sheet pan. The toffee melts into sticky bits and sticks to the bottom of the sheet pan, making removing the cookies somewhat difficult.
*9 The baking time varies, depending on the oven and cookie sheet. Some ovens are hotter than others and some cookie sheets heat up more quickly than others. I tested these cookies in 3 different ovens and on 3 different baking sheets. Each time, the baking time varied slightly. For the first batch, I recommend setting a timer for 7 minutes and checking the cookies for doneness. After checking, add 1 minute to the timer until the cookies are firm and crispy looking on the edges and soft in the middle. The cookies will also be puffy when you first pull them out of the oven but will "collapse" as they cool.
**This is a (slightly) modified version of Bon Appetit's Brown Butter and Toffee Chocolate Chip cookies. I substituted toffee bits for chopped up Skor bar, chocolate chips for chocolate wafers/discs. I also added more vanilla and less (white) sugar. Basically, my version is a plebian, grocery store version that's hopefully more accessible.
***Toffee bits can be found in the baking aisle. I use Hershey's toffee bits, also labeled Skor bits.