Place water, garlic, milk, salt, cayenne and paprika in a nonreactive saucepot and heat until it boils.
Lower heat to gentle simmer and whisk in chickpea flour. Whisk just until smooth and then use a high-heat spatula to finish the process. Cook mixture for about 5 minutes, constantly stirring to make sure there is no scorching.
Once flour is nearly cooked, fold in chopped chickpeas, Parmesan cheese and extra virgin olive oil. Stir until well incorporated and hot. This should take about 3 additional minutes.
Place in a plastic wrap-lined 10-by-12-inch tray. Cover with plastic wrap and push down so it is even. Chill for at least 2 hours in the refrigerator or until completely chilled.
After well-chilled, turn the chickpea mold onto a cutting board. Cut fries 12 times in 1-inch pieces and then cut each strip into 4 pieces, forming 48 pieces. Heat canola oil in a large stainless steel fry pot to 350 degrees. Dust fries with remaining chickpea flour and fry in 4 batches until hot and golden brown.
Drain in paper towels to remove excess oil. Serve immediately with Orange Preserved Lemon Dipping Sauce (recipe follows).