To make chickpea spread, to food processor or high-speed blender, add chickpeas, yeast, lemon juice, and seasonings. Whirl on and off at high speed until crumbly. Add 1/4 cup water and continue to whirl at high speed, occasionally scraping down sides of bowl with spatula. Add a little more water if needed, until mixture is very smooth and creamy and of spreadable consistency. Transfer to tightly covered container and refrigerate until ready to use. Chickpea spread can be refrigerated for up to 1 week.
To make creamy yogurt cheese, line fine-mesh sieve with several layers of cheesecloth. Straddle over top of bowl, leaving generous space between bottom of bowl and the sieve. Spoon yogurt into lined sieve. Place in refrigerator for up to 2 days, until yogurt has drained out liquid whey, leaving a thickened yogurt cheese in sieve. Discard whey or store in refrigerator and use for another recipe (e.g. in baking). Transfer yogurt cheese to clean bowl and stir in remaining ingredients to blend. Transfer to tightly covered container and store in refrigerator for up to 1 week.
To serve, spread chickpea mixture or seasoned yogurt cheese on bread slices or crackers and garnish with desired toppings.