Preheat the oven to 400°F. To make cleanup easier, line a rimmed baking sheet with parchment paper or foil. Set aside.
Cut each jalapeño pepper in half. Using a spoon (a grapefruit spoon works really well here), scrape out the seeds and white parts and discard. Set the halved, seeded peppers aside.
*NOTE* If you have latex (or similar) gloves, wear them! You don't want to accidentally rub your eyes after handling jalapeños, trust me.
Combine the cream cheese, shredded cheddar, minced garlic, and smoked paprika in a mixing bowl. Using a wooden spoon or silicone spatula, combine everything together until the mixture is smooth and even.
Fill each jalapeño half with the cream cheese mixture, slightly overfilling and smoothing the mixture on top. Once all peppers are stuffed, wrap 1 slice of bacon around each one, leaving the ends of the bacon on the bottom of the pepper. Secure the bacon with a toothpick to keep it from unwrapping as it bakes.
Arrange the prepared peppers on the lined baking sheet so they are close but not touching. Bake in the preheated oven for 25 minutes, or until the bacon is crispy and the cream cheese filling has browned on top and is bubbly.
Remove from the oven and let cool slightly before serving. Garnish with additional smoked paprika, if desired.