In a heavy-bottomed saucepan, bring the water, olive oil, and salt to a simmer.
Gradually whisk in the chickpea flour to avoid lumps.
Keep whisking constantly over medium-low heat for about 10–15 minutes, until the mixture thickens and becomes smooth and glossy (like thick polenta). It should pull away from the sides of the pan.
Pour the mixture into a greased or parchment-lined rectangular dish or baking sheet (about 1 to 1.5 inches thick).
Smooth the top and let it cool at room temperature, then refrigerate for at least 12 hours (or overnight) until fully set.
Once firm, cut into fries, rectangles, or wedges.
Heat a generous amount of olive oil in a nonstick or cast-iron skillet over medium-high heat.
Fry the pieces until golden and crisp on all sides, about 3–5 minutes per side.
Drain on paper towels and season with salt and pepper.
Serve hot, with more black pepper, optionally with a tapenade dip or just a squeeze of lemon.
