For the Buñuelos: In saucepan, bring water, sugar, and liqueur (if using) to simmer over medium heat, stirring until sugar dissolves. Remove from heat and cover to keep warm.

Combine flour, baking powder, and salt in large bowl. Using fingertips, rub lard or butter into flour mixture until mixture is crumbly. Work eggs in with fingertips until incorporated, then gradually add the warm sugar water, adding enough to make a cohesive dough.

Knead the dough on a clean, dry work surface until smooth, 10 to 15 minutes.

Cover dough and let rest at room temperature for 1 hour.

Meanwhile, cover a clean, dry work surface with several clean kitchen towels.

Divide the dough into approximately 1-inch pieces and roll each one into a ball. Using a rolling pin (dough should be smooth but not sticky—flouring the work surface is not necessary), roll each ball into a 6- to 7-inch diameter circle—each buñuelo should be thin enough to be translucent.

Arrange the dough circles on the towel-lined surface and let rest 45 minutes. Turn the circles and allow to dry an additional 45 minutes. Dough will feel papery to the touch after the drying period.

Line 2 baking sheets with 2 layers paper towels. Heat oil in a Dutch oven or large skillet with high sides over medium-high heat until temperature registers 350°F. (Oil should be 1- to 1 1/2 inches deep). Fry buñuelos 1 to 2 at a time until golden on one side, 30 to 60 seconds. Turn over with tongs, and fry until opposite side is golden, 30 to 45 seconds.

Transfer to prepared trays and repeat with remaining dough.

For the syrup: Combine piloncillo, brown sugar, or sugar, water, cinnamon and aniseeds to boil over medium- high heat in medium heavy-bottomed saucepan, stirring until sugar is dissolved. Reduce heat to medium and simmer until mixture is syrupy, 5-to-7 minutes. Strain syrup, discard solids and drizzle over buñuelos or serve alongside.

Serve buñuelos with warm syrup.