Preheat the oven to 350°F.
Bring a large pot of water to a boil. Add some salt and oil.
Wash the green figs, trim off both ends, and score the skin lengthwise.
Add the green figs to the boiling water and cook until fork-tender.
While the figs are boiling, melt the butter in a deep saucepan over medium heat. Gradually whisk in the flour and cook for 1–2 minutes, stirring continuously.
Slowly add the milk, a little at a time, whisking to prevent lumps. Pour in the broth and continue stirring until combined.
Add the shredded cheese and stir until melted.
Stir in the minced garlic, pimento peppers, salt, and black pepper.
Simmer over medium-low heat, stirring occasionally, until the sauce thickens. Remove from the heat.
Once the green figs are tender, drain and allow them to cool enough to handle. Peel and cut them into smaller pieces.
Transfer the green figs to a large bowl and roughly mash them with a fork or potato masher, leaving some small chunks for texture.
Pour the cheese sauce over the mashed green figs and mix until well combined. Taste and adjust the salt and black pepper as needed.
Transfer the mixture to a greased baking dish and spread evenly.
Sprinkle the remaining shredded cheese over the top, followed by the breadcrumbs, if using.
Bake for approximately 25–30 minutes, until the topping is melted and golden brown.
Remove from the oven and let the pie rest for 10–15 minutes before cutting and serving.