Preheat the oven to 175 C. Spread the pecans out in a single layer on an un-greased baking tray. Bake for 5 to 7 minutes, until fragrant. Allow them to cool completely, then chop coarsely and set aside.
To brown the butter (I do this while the pecans are cooling), place it in a saucepan (if it has a light coloured base, that's easier to see the browning) that's fairly deep because the butter will foam up! Set the saucepan on low heat and let the butter melt, stirring often. It will start to bubble and foam up vigorously, so keep an eye on it, stirring almost continuously at this stage to prevent burning.
The milk solids will start to separate and you'll hear a sizzling sound. After 3 to 4 minutes, the butter will begin to smell nutty and toasty and you'll see the milk solids browning a little on the sides and the bottom and the surface looking a deep amber, golden colour. I prefer to take it to the edge and let the solids darken a fair bit (see post and photos above for more info), then take it off the heat and immediately pour into a mixing bowl so it doesn't keep cooking in the hot pan. Set aside to cool at room temperature for 10 minutes.
Then add the sugars to the browned butter and whisk to combine thoroughly. Add the egg and vanilla and whisk again (I use a balloon whisk) till incorporated.
Sift in the flour, baking soda, baking powder and salt, if using. Fold to combine into a soft dough, which will look a little greasy because of the melted butter. Add the chopped toasted pecans and the chocolate chips and stir them gently into the dough, using your hands if needed to bring it all together.
Cover the bowl with clingfilm and chill it for 30 minutes. If chilling for an hour or longer, the dough will need to sit at room temperature before you are able to scoop it. Keep in mind the colder the dough, the puffier the cookies will be.
Preheat the oven to 175 C again. Line a baking tray (or two if you're baking in batches) with silicone baking mats. Set aside.
Using a cookie scoop, make equal-sized portions (1.5 tablespoons each) of the dough and place them on the baking tray, at least two inches apart. You could also use a spoon if you don't have a cookie scoop. The dough might seem a little crumbly at first so use your fingers if needed to shape the individual dough balls and press the pecans and chocolate chips in.
Bake for 10 to 12 minutes until the cookies are lightly browned on the edges and still puffy in the middle. Take the tray out of the oven and very gently, press down on each cookie with the back of a spoon or a metal spatula to flatten further. Allow the cookies to cool and firm up for 10 minutes at room temperature on the tray itself, then transfer to a wire rack to cool completely. Bake for 15 minutes if you prefer firmer, darker cookies but keep in mind, that as cookies cool, they continue to bake and firm up, so don't leave them in the oven for too long.
Store in an airtight tin at room temperature for 4 to 5 days (I think these are best in the first couple of days). In the fridge, they'll last about 2 weeks and longer in the freezer. Happy baking!