Preheat the oven to 350 degrees (for the crackers).
To pickle the jalapeno, combine the vinegar, water, sugar, and 1 teaspoon kosher salt in a microwave safe cup or bowl, and heat on high 1 to 2 minutes, until boiling. Stir to dissolve. Stir in the jalapeno pieces and set aside for about 10 minutes, stirring once or twice (the peppers will lighten slightly in color). Drain and discard liquid.
Meanwhile, heat a small skillet over medium-high heat and add the garlic cloves. Roast, turning cloves once or twice, until lightly browned and softened. Remove and cool slightly before removing the skins and tough stem ends.
While those items are underway, add 1 tablespoon of olive oil, lime juice, spinach, avocado, parsley, paprika, and ½ teaspoon kosher salt to a blender. When the garlic and peppers are done, add them to the blender as well and process until smooth. The mixture might be hard to blend at first; stop and scrape down the sides every 10 seconds or so and add more oil, a few drops at a time as needed, to get the mixture to become smooth. The dip is best served right away but can be refrigerated for up to 24 hours (stir in any liquid that separates out) before serving.
To make the crackers, line two large rimmed baking sheets with aluminum foil. Place the crackers in a large sealable bag or a large bowl and toss with olive oil to coat. Spread crackers in a single layer on the two prepared pans. Sprinkle the tops evenly with chili powder, onion powder, and paprika, and finish with a light sprinkle of kosher salt.
Bake in the 350-degree oven for about 8 minutes, rotating the pans halfway through, until the crackers are mostly dry and the spices very fragrant. Remove and serve warm with dip, or let come to room temperature and store in a sealed bag until ready to use.