Heat 1 Tbsp. of the oil in a large nonstick skillet over medium. Add eggplant; cook 6 to 8 minutes, stirring occasionally, until golden and soft. Season with 1/4 tsp. each of the salt and pepper, plus a pinch of crushed red pepper flakes. Set aside.
Add an additional 1 Tbsp. oil to the pan and increase heat to medium-high. Pat halloumi dry and add to pan in a single layer. Cook, turning once, until golden brown, 1 1/2 to 4 minutes total. Transfer to a plate.
Combine remaining 1 Tbsp. olive oil with lemon juice, dill, mustard, garlic powder, and remaining 1/4 tsp. salt and black pepper; stir with a whisk. Whisk in yogurt in 1 Tbsp. increments until smooth.
To assemble bowls, divide farro evenly into each of 4 bowls. Top evenly with cooked eggplant and halloumi cheese. Add tomatoes, cucumber, and chickpeas evenly to each bowl. Drizzle each serving with 1-2 Tbsp. lemon-dill sauce. Garnish with extra dill, if desired.