Preparation

Make the ice cream

• In an 8- or 9-inch skillet, toast the chiles over medium heat, pressing them flat against the skillet with a metal spatula, until fragrant, about 10 seconds per side. Transfer to a 2-quart saucepan, and add the half-and-half and both chocolates. Bring to a simmer over medium heat, stirring frequently. Remove from the heat, cover, and let steep for 10 minutes. Transfer to a blender and purée.
• In a 4-quart saucepan, bring 3 inches of water to a simmer over medium-low heat.
• Put the egg yolks in a heatproof bowl that will fit over the saucepan without touching the water and whisk off the heat to loosen. Add the sugar and whisk until well combined. Whisking constantly, slowly pour the chocolate mixture into the eggs. Put the bowl over the simmering water and whisk, frequently scraping down the sides of the bowl with a spatula, until the mixture thickens and registers 180°F on an instant-read thermometer, about 5 minutes.
• Strain the mixture through a fine-mesh strainer into a clean bowl. Refrigerate until thoroughly chilled, at least 4 hours or up to 1 day, covering once cold. If you want to freeze the ice cream right away, nestle the bowl in a larger bowl of ice water and whisk until cold (40°F is best), 4 to 6 minutes.
• Stir in the cream, beer, and vanilla.
• Freeze in an ice cream maker according to the manufacturer’s directions. Transfer to a container and freeze until firm, several hours or overnight.

Make the sauce

• In a 4-quart saucepan, bring the sugar, agave, and 1/4 cup water to a boil over medium-high heat. Lower the heat to medium and cook, stirring frequently, until the sugar dissolves, 2 to 3 minutes. Cover, reduce the heat to low, and simmer for 1 minute without stirring.
• Remove from the heat and stir in the chocolate and salt. Let stand until the chocolate melts, then whisk until smooth. Add the cocoa and whisk until smooth. Add the cream, butter, chile powder, vanilla, cinnamon, and cayenne, and stir until combined. Serve the sauce hot.

Store leftover sauce in a tightly covered jar in the refrigerator for up to 10 days. Reheat in a microwave oven or place the open jar in a pot of simmering water, stirring frequently, until hot.