Adjust the oven rack so it is 6 inches from the broiler element. Heat the broiler on high. Place the eggplant on a baking sheet and rub all over with 1 Tbs. of the olive oil. Broil skin side up until the skin is completely charred, about 8 minutes. Flip the eggplant and broil until the flesh is nicely browned and softened, about 3 minutes more. Set the eggplant aside to cool.

Heat the remaining 6 Tbs. olive oil and the garlic in a medium saucepan over medium-low heat until just sizzling and slightly browned at the edges, about 3 minutes. Add the beans, anchovies, rosemary, salt, and pepper flakes. Simmer to infuse the flavors, about 5 minutes.

Peel the charred skin off the eggplant. Put the flesh in the bowl of a food processor with the bean mixture and the lemon juice. Process until smooth. Spoon the dip into serving bowl. Drizzle additional olive oil on top and sprinkle with rosemary leaves and crushed red pepper flakes. Serve warm, chilled or at room temperature with toasted rustic bread or crackers.