In bowl of standing mixer fitted with paddle attachment, beat butter at medium speed until smooth and creamy. Beat in sugars until combined, about 45 seconds; mixture will look granular. Reduce speed to low and gradually beat in egg mixture until incorporated, about 45 seconds. Add melted chocolate and chips in steady stream and beat until combined, about 40 seconds. Scrape bottom and sides of bowl with rubber spatula. With mixer at low speed, add dry ingredients and mix until just combined. Do not over-beat.
Cover with plastic wrap and let stand at room temperature until consistency is scoopable and fudge-like, about 30 minutes.
Meanwhile, adjust oven racks to the upper-middle and lower-middle positions and heat oven to 350 degrees. Line two baking sheets with parchment paper. Leaving about 1 1/2 inches between each ball, scoop dough onto parchment-lined cookie sheets with 1 3/4-inch ice cream scoop (use a #40 portion scoop).
Bake, reversing position of the baking sheets halfway through baking (from top to bottom and front to back), until edges of cookies have just begun to set but centers are still very soft, about 10 minutes. Cool cookies on sheets about 10 minutes, slide parchment with cookies onto wire racks, and cool to room temperature.