Place the butter in a small saucepan over medium-high heat and cook, stirring almost constantly, until the butter browns and develops toasted bits, about 3 minutes.
Pour the browned butter (including all toasted bits) into a heatproof bowl and scrape the pan. Let the butter cool at room temperature until it is not liquid and a light indentation remains when you press the surface with a finger. If you need to speed this up, briefly chill the bowl in the refrigerator until the butter firms, then return it to room temperature so it is soft but not liquid.
When the butter is ready, preheat the oven to 375°F (190°C). Line two large baking sheets with parchment paper and set aside.
In a large bowl, whisk together the flour, salt, and baking soda until combined; set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl using a handheld electric mixer, combine the cooled browned butter, dark brown sugar, and granulated sugar. Beat on medium speed until light and fluffy, about 2 minutes.
Add the almond extract and the amaretto to the butter mixture and beat just until combined.
Add the eggs one at a time, beating about 15 seconds after each addition until incorporated.
Turn the mixer off. Using a wooden spoon or sturdy rubber spatula, gently fold in the flour mixture only until the flour begins to disappear; do not overmix.
Fold in the chopped chocolate chunks and the sliced almonds until evenly distributed.
For extra-thick cookies, chill the dough for at least 2 hours (or up to 3 days) before baking. For thinner cookies, bake the dough right away.
Roll 3-tablespoon-sized scoops of dough between your palms to form balls (they should be almost 1/4 cup each). Place the balls on the prepared baking sheets, leaving at least 2 inches between each cookie for spreading.
Bake the cookies one sheet at a time in the preheated oven for 9 to 10 minutes, or until the edges are golden and the centers still look soft.
Let the cookies cool on the baking sheet for 10 minutes, then transfer them to a wire rack to cool completely. Repeat baking with remaining dough.