Cook and stir bacon with 1/4 cup vegetable in a skillet over medium heat until bacon is browned and crisp, 5 to 7 minutes. Pour bacon into a strainer set over a bowl, reserving 1/3 cup of bacon drippings.
Return skillet to medium heat. Stir onions and salt into the skillet; cook and stir until onions are golden brown, about 5 minutes. Stir in garlic; cook, stirring constantly, until the garlic is fragrant and golden, 1 minute.
Stir cider vinegar, rice vinegar, 1/2 cup water, sugar, and Dijon mustard into onion mixture. Increase heat to medium-high and simmer.
Whisk 2 teaspoons water and cornstarch in a bowl. Gradually pour cornstarch mixture into onion mixture and whisk until thickened. 3 to 4 minutes. Reduce heat to low.
Drizzle reserved 1/3 cup bacon drippings into onion mixture, whisking constantly. Add cooked bacon and stir to combine. Season with cayenne pepper, salt, and black pepper to taste.
Combine spinach, black-eyed peas, mushrooms, and cherry tomatoes in a large bowl; toss to combine. Drizzle hot bacon dressing over spinach mixture; toss quickly and serve immediately.
