Step 1: In a large mixing bowl, whisk together the flour, sugar, baking powder, ground cardamom, and salt until well combined.
Step 2: In a separate medium bowl, whisk the Greek yogurt, egg, melted butter, and vanilla extract until smooth.
Step 3: Pour the wet ingredients into the dry ingredients and stir with a spatula until just combined. The dough for your pear and cardamom donut holes should be thick and slightly sticky.
Step 4: Gently fold in the finely diced pears, ensuring they are distributed evenly without overworking the batter.
Step 5: Heat about 2 inches of vegetable oil in a heavy-bottomed pot or Dutch oven until it reaches 350°F (175°C).
Step 6: Use a small cookie scoop or two spoons to drop rounded tablespoons of the pear and cardamom donut holes batter into the hot oil. Fry 5-6 at a time to avoid crowding.
Step 7: Fry for 2-3 minutes, turning occasionally with a slotted spoon, until the pear and cardamom donut holes are golden brown on all sides.
Step 8: Remove the pear and cardamom donut holes from the oil and place them on a paper towel-lined plate to drain.
Step 9: While warm, whisk the honey and warm water together and lightly brush over the donut holes or toss them gently in the glaze before serving.