Add all the ingredients to a small bowl and combine well. Set aside.
Heat a large nonstick skillet or a cast iron griddle over medium-high heat. Spread 1 side of each tortilla with butter. Lay 2 tortillas in the pan, buttered side down, and top each with half of the chocolate in a random order of varieties. Sprinkle each with 1 teaspoon cocoa chili powder and cover with the remaining tortillas, buttered side up. Let cook until the chocolate starts to melt, about for 3 to 4 minutes. Carefully flip over and cook the other side until evenly browned, an additional 3 to 4 minutes. Remove from heat to a cutting board, let rest for 3 to 4 minutes, then cut each into 4 quarters. To plate, put 1 scoop of ice cream into each serving dish, add 2 pieces of quesadilla and drizzle with the dark chocolate sauce. Dust each dish evenly with remaining teaspoon of the cocoa chili powder. Serve immediately.