Line a baking sheet with parchment paper or a silicone baking mat. If neither is available, lightly grease with oil.

In a medium heavy-duty skillet, spread 2/3 cup granulated sugar in an even layer. Heat over medium-high heat. As the sugar begins to liquefy, stir with a heatproof spatula, folding in any undissolved sugar.

Continue cooking and stirring carefully until the sugar reaches a deep amber color and begins to smoke slightly. Remove from heat immediately.

Quickly scrape the mixture onto the lined baking sheet and swirl sheet to prevent clumping. Let it cool until firm and crisp, then chop into bite-sized pieces.

In a stand mixer fitted with the paddle attachment, beat the cubed butter, remaining 1/3 cup granulated sugar, and brown sugar on medium speed until smooth (not fluffy).

Mix in the remaining 3/4 teaspoon salt, vanilla extract, and egg until just combined. Scrape down the sides of the bowl as needed.

In a separate bowl, whisk together the flour, baking soda, and baking powder. Gradually add this dry mixture to the butter mixture on low speed until just incorporated.

Fold in the chopped chili brittle and chocolate until evenly distributed.

Preheat your oven to 350°F (180°C). Line 1 to 2 baking sheets with parchment paper.

Using a spring-loaded ice cream scoop or two spoons, shape the dough into 1 1/2-inch (4 cm) rounds, placing them 2 inches (5 cm) apart on the baking sheets. Optionally, roll the dough in your hands for neater cookie shapes.

Bake the cookies for 10 to 12 minutes, rotating the sheets halfway through, until golden brown around the edges.