Combine water, 1/4 cup vegetable oil, brown sugar, salt, and vanilla in a 4 quart saucepan and bring to a boil, stirring to dissolve sugar and salt.

Remove from heat, add flour and cocoa and stir with a wooden spoon until smooth. Let cool slightly (about 5 minutes) then add egg and beat into the mixture until fully incorporated.

Cover a baking sheet with parchment paper or a Silpat silicone sheet and spray with baking spray. Transfer dough to the piping bag fitted with the star attachment and pipe into a 10-inch long rope on the prepared sheet. Bend rope to form a heart shape, squeezing the two ends together so they stick and creating a point at the other end. Repeat with the remaining dough.

Combine vegetable oil and lard in a large Dutch oven or deep cast iron pot and attach a deep fat fry thermometer to the side.

Line a baking sheet with a couple layers of paper towels. Combine granulated sugar and cinnamon in a large, wide bowl.

Once oil reaches 375°F add 2-3 churro hearts at a time and fry until crisped, about 2 minutes. Flip and continue to fry 1 more minute on the other side. Watch the oil temperature and raise or lower the heat to keep it as steady as possible.

Remove churros with a bamboo skimmer or tongs to the paper towel-lined sheet. Let cool about a minute then dip in the cinnamon-sugar mixture to coat both sides. Set back on the baking sheet to cool. Repeat with remaining churro hearts.

Combine dulce de leche, Licor 43, and salt in a small saucepan. Heat, stirring occasionally until sauce is smooth and well combined. Remove from heat, transfer to a serving bowl and serve warm with the churros.