1. Dough: Stir together the flour, cocoa, and salt in a medium bowl. Add 1 cup of the toffee chips and toss with the mixture.
2. In a separate big bowl, beat the butter and granulated sugar together on medium speed until fluffy. Add the egg and vanilla and beat until combined.
3. Add the flour mixture and stir with a spoon. Make sure the toffee pieces are evenly dispersed.
4. Roll the dough into 1 ½-inch balls and place on parchment-lined baking sheets. Use your thumb or a spoon to press a well into the center of each one. Refrigerate the cookies for at least 45 minutes.
5. Preheat the oven to 350°. Make sure the cookies are about an inch apart. Return any remaining cookies to the refrigerator until ready to bake.
6. Bake for 8-10 minutes. Cool completely on the baking sheet and then transfer to a cooling rack. Repeat until all the cookies are baked.
7. Filling: Place the chocolate chips and butter in a small, heat-proof bowl.
8. Heat the heavy cream in a small saucepan over medium-high heat, stirring often, until it comes to a boil.
9. Pour the cream over the chocolate chips and cover the bowl tightly with aluminum foil. Let it sit for 5-6 minutes, then whisk until the chocolate is completely melted and smooth. Add the sugar and whisk until smooth and creamy.
10. Spoon the filling into the indentations on the cookies and sprinkle with the remaining toffee chips. Let set for about an hour.
